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Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Jinyi Sun, Chunlan Liu, Minghua Yang
The paper is concerned with the three-dimensional Boussinesq-Coriolis equations with Caputo time-fractional derivatives. Specifically, by striking new balances between the dispersion effects of the Coriolis force and the smoothing effects of the Laplacian dissipation involving with a time-fractional evolution mechanism, we obtain the global existence of mild solutions to Cauchy problem of three-dimensional
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Transformations of the matrices of the fractional linear systems to their canonical stable forms Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Tadeusz Kaczorek, Lukasz Sajewski
A new approach to the transformations of the matrices of the fractional linear systems with desired eigenvalues is proposed. Conditions for the existence of the solution to the transformation problem of the linear system to its asymptotically stable controllable and observable canonical forms with desired eigenvalues are given and illustrated by numerical examples of fractional linear systems.
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Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26
Abstract This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [3, 4] or Addendum to [22]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for
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Relative controllability of linear state-delay fractional systems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-25
Abstract In this paper, our focus is on exploring the relative controllability of systems governed by linear fractional differential equations incorporating state delay. We introduce a novel counterpart to the Cayley-Hamilton theorem. Leveraging a delayed perturbation of the Mittag-Leffler function, along with a determining function and an analog of the Cayley-Hamilton theorem, we establish an algebraic
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Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-25 Leijie Qiao, Wenlin Qiu, M. A. Zaky, A. S. Hendy
In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution problems. A theta-type (\(\theta \)-type) convolution quadrature rule is derived to approximate the nonlocal integral term in the problem under consideration, such that \(\theta \in (\frac{1}{2},1)\), which remains untreated in the literature. The proposed
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-22
Abstract In this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment \(h>0\) , can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all \(h>0\) the discretization. It is
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Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$ Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-20 Truong Vinh An, Vasile Lupulescu, Ngo Van Hoa
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Rich phenomenology of the solutions in a fractional Duffing equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-20 Sara Hamaizia, Salvador Jiménez, M. Pilar Velasco
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Sum of series and new relations for Mittag-Leffler functions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-19 Sarah A. Deif, E. Capelas de Oliveira
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-11 Hassan Askari, Alireza Ansari
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Global optimization of a nonlinear system of differential equations involving $$\psi $$ -Hilfer fractional derivatives of complex order Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-11
Abstract In this paper, a class of cyclic (noncyclic) operators of condensing nature are defined on Banach spaces via a pair of shifting distance functions. The best proximity point (pair) results are manifested using the concept of measure of noncompactness (MNC) for the said operators. The obtained best proximity point result is used to demonstrate existence of optimum solutions of a system of differential
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Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-05
Abstract In this work we study the following nonlocal problem $$\begin{aligned} \left\{ \begin{aligned} M(\Vert u\Vert ^2_X)(-\varDelta )^s u&= \lambda {f(x)}|u|^{\gamma -2}u+{g(x)}|u|^{p-2}u{} & {} \text{ in }\ \ \varOmega , \\ u&=0{} & {} \text{ on }\ \ \mathbb R^N\setminus \varOmega , \end{aligned} \right. \end{aligned}$$ where \(\varOmega \subset \mathbb R^N\) is open and bounded with smooth boundary
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Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-04 Nikola Kosturski, Svetozar Margenov
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Analysis of a class of completely non-local elliptic diffusion operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-29
Abstract This work explores the possibility of developing the analog of some classic results from elliptic PDEs for a class of fractional ODEs involving the composition of both left- and right-sided Riemann-Liouville (R-L) fractional derivatives, \({D^\alpha _{a+}}{D^\beta _{b-}}\) , \(1<\alpha +\beta <2\) . Compared to one-sided non-local R-L derivatives, these composite operators are completely non-local
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Discrete convolution operators and equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27
Abstract In this work we introduce discrete convolution operators and study their most basic properties. We then solve linear difference equations depending on such operators. The theory herein developed generalizes, in particular, the theory of discrete fractional calculus and fractional difference equations. To that matter we make use of the so-called Sonine pairs of kernels.
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Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Zuomao Yan
We study the approximate optimal control for a class of fractional stochastic hemivariational inequalities with non-instantaneous impulses driven by Rosenblatt process in a Hilbert space. Firstly, a suitable definition of piecewise continuous mild solution is introduced, and by using stochastic analysis, properties of \(\alpha \)-order sine and cosine family and Picard type approximate sequences, we
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Optimal control of fractional non-autonomous evolution inclusions with Clarke subdifferential Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Xuemei Li, Xinge Liu, Fengzhen Long
In this paper, the non-autonomous fractional evolution inclusions of Clarke subdifferential type in a separable reflexive Banach space are investigated. The mild solution of the non-autonomous fractional evolution inclusions of Clarke subdifferential type is defined by introducing the operators \(\psi (t,\tau )\) and \(\phi (t,\tau )\) and V(t), which are generated by the operator \(-\mathcal {A}(t)\)
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A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26
Abstract In this article, we focus on the application of the recent notion of time-fractional derivative developed in Sobolev spaces to the study of well-posedness and stability for a time-fractional wave-like equation with superdiffusion and subdiffusion terms.
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Schrödinger-Maxwell equations driven by mixed local-nonlocal operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26
Abstract In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter
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The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26
Abstract In this work we study the Riemann-Liouville fractional integral of order \(\alpha \in (0,1/p)\) as an operator from \(L^p(I;X)\) into \(L^{q}(I;X)\) , with \(1\le q\le p/(1-p\alpha )\) , whether \(I=[t_0,t_1]\) or \(I=[t_0,\infty )\) and X is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from
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Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-23 Zhiwei Hao, Libo Li, Long Long, Ferenc Weisz
Let \(0
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Operational matrix based numerical scheme for the solution of time fractional diffusion equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-23 S. Poojitha, Ashish Awasthi
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Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22
Abstract This study investigates the inverse problem of determining the right-hand side of a telegraph equation given in a Hilbert space. The main equation under consideration has the form \((D_{t}^{\rho })^{2}u(t)+2\alpha D_{t}^{\rho }u(t)+Au(t)=p( t)q+f(t)\) , where \(0
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Generalized Krätzel functions: an analytic study Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Ashik A. Kabeer, Dilip Kumar
The paper is devoted to the study of generalized Krätzel functions, which are the kernel functions of type-1 and type-2 pathway transforms. Various analytical properties such as Lipschitz continuity, fixed point property and integrability of these functions are investigated. Furthermore, the paper introduces two new inequalities associated with generalized Krätzel functions. The composition formulae
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On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan D. Repovš
We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there
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Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-21 Ziqiang Li, Yubin Yan
We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The equation involves the \(\psi \)-Caputo derivative of order \(\alpha \in (0,1)\) and the spectral fractional Laplacian of order \(\beta \in (\frac{1}{2},1]\). The existence and uniqueness of the mild solution are proved in a suitable Banach space by using the
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Asymptotic behavior for a porous-elastic system with fractional derivative-type internal dissipation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-21 Wilson Oliveira, Sebastião Cordeiro, Carlos Alberto Raposo da Cunha, Octavio Vera
This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem
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Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-20
Abstract The purpose of this paper is to consider the fractional delayed evolution equation of order \(\gamma \in (1,2)\) in ordered Banach space. In the absence of assumptions about the compactness of cosine families or related sine families, the existence results of positive solutions are studied by using some fixed point theorems and monotone iterative method under the conditions that nonlinear
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Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-16
Abstract In this paper, we consider the following problem $$\begin{aligned} {\left\{ \begin{array}{ll} (-\varDelta )^{s} u=g(x) u^{2_{s}^{*}-1}+\lambda u^{-\gamma }, &{} \text { in } \varOmega , \\ u>0, \text { in } \varOmega , \quad u=0, &{} \text { on } \partial \varOmega , \end{array}\right. } \end{aligned}$$ where \(\varOmega \subset {\mathbb {R}}^{N}(N > 2s)\) is a smooth bounded domain, \(s\in
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Some boundedness results for Riemann-Liouville tempered fractional integrals Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-16 César E. Torres Ledesma, Hernán A. Cuti Gutierrez, Jesús P. Avalos Rodríguez, Willy Zubiaga Vera
In this work we generalize some results of the Riemann-Liouville fractional calculus for the tempered case, namely, we deal with some boundedness results of Riemann-Liouville tempered fractional integrals on continuous function space and Lebesgue spaces in bounded intervals and on the real line. Moreover, the limit behavior of the Riemann-Liouville tempered fractional integrals approaching to the Riemann-Liouville
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Representations of solutions of systems of time-fractional pseudo-differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-16 Sabir Umarov
Systems of fractional order differential and pseudo-differential equations are used in modeling of various dynamical processes. In the analysis of such models, including stability analysis, asymptotic behaviors, etc., it is useful to have a representation formulas for the solution. In this paper we prove the existence and uniqueness theorems and derive representation formulas for the solution of general
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Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-14 K. S. Vishnukumar, M. Vellappandi, V. Govindaraj
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Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-25 Yu He, Qi Sun, Ciqiang Zhuo
Let \(p(\cdot ),\ q(\cdot )\) and \(\alpha (\cdot )\) be variable exponents satisfying some Hölder continuous conditions. In this paper, the authors characterize the variable inhomogeneous Besov space \(B_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}(\mathbb {R}^n)\) and the variable inhomogeneous Triebel-Lizorkin space \(F_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}(\mathbb {R}^n)\) in terms of Hajłasz gradient
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Log-concavity and log-convexity of series containing multiple Pochhammer symbols Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-22 Dmitrii Karp, Yi Zhang
In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the Pochhammer symbols. Four types of such series are treated. We show that logarithmic concavity (convexity) of the generic sequence leads to logarithmic concavity (convexity) of the sum of the series with respect to the argument
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Decay estimates and extinction properties for some parabolic equations with fractional time derivatives Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-16 Tahir Boudjeriou
The main goal of this paper is to study the asymptotic behaviour and the finite extinction time of weak solutions to some time-fractional parabolic equations. Moreover, we improve some results in [5, 10] by dropping out some conditions assumed there.
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Lump solutions of the fractional Kadomtsev–Petviashvili equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-10 Handan Borluk, Gabriele Bruell, Dag Nilsson
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A mutually exciting rough jump-diffusion for financial modelling Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-02 Donatien Hainaut
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On some even-sequential fractional boundary-value problems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-01-02 Ekin Uğurlu
In this paper we provide a way to handle some symmetric fractional boundary-value problems. Indeed, first, we consider some system of fractional equations. We introduce the existence and uniqueness of solutions of the systems of equations and we show that they are entire functions of the spectral parameter. In particular, we show that the solutions are at most of order 1/2. Moreover we share the integration
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Pricing Vulnerable Options in Fractional Brownian Markets: a Partial Differential Equations Approach Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-29 Takwon Kim, Jinwan Park, Ji-Hun Yoon, Ki-Ahm Lee
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Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-22
Abstract As a follow-up to the inherent nature of Caputo-Hadamard fractional derivative (CHFD) and the Hadamard fractional derivative ( HFD), little is known about some asymptotic behaviors of solutions. In this paper, a system of fractional differential equations including two types of fractional derivatives the CHFD and the HFD is investigated. The leading derivative is of an order between zero and
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On the Filippov-Ważewski relaxation theorem for a certain class of fractional differential inclusions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-21 Jacek Sadowski
The purpose of this text is to propose an attempt of an extension of the Filippov-Ważewski Relaxation Theorem for a certain class of fractional differential inclusions. The classical result devoted to ordinary differential inclusions is a part of the qualitative theory: a description of the relationship between the solutions to the differential inclusion and the convexified differential inclusion was
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Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-20 Anatoly A. Alikhanov, Mohammad Shahbazi Asl, Chengming Huang
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the development of a numerical method and analysis, the original problem is transformed into a new integro-differential model which includes the Caputo derivatives and the Riemann-Liouville fractional integrals with orders belonging
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Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-20
Abstract A fully implicit numerical scheme is established for solving the time fractional Swift-Hohenberg equation with a Caputo time derivative of order \(\alpha \in (0,1)\) . The variable-step L1 formula and the finite difference method are employed for the time and the space discretizations, respectively. The unique solvability of the numerical scheme is proved by the Brouwer fixed-point theorem
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A class of Hilfer fractional differential evolution hemivariational inequalities with history-dependent operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-06 Zhao Jing, Zhenhai Liu, Nikolaos S. Papageorgiou
The main purpose of this paper is to study an abstract system which consists of a parabolic hemivariational inequality with a Hilfer fractional evolution equation involving history-dependent operators, which is called a Hilfer fractional differential hemivariational inequality. We first show existence and a priori estimates for the parabolic hemivariational inequality. Then, by using the well-known
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Robust model predictive control for fractional-order descriptor systems with uncertainty Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-01 Adnène Arbi
In this study, a new robust predictive control technique is investigated for uncertain fractional-order descriptor systems. Using the properties of fractional calculus and the construction of an appropriate Lyapunov function, the sufficient conditions to guarantee the existence of a robust predictive controller are given by minimizing the worst-case optimization problem. The new robust predictive controller
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Least energy sign-changing solutions for fractional critical Kirchhoff–Schrödinger–Poisson with steep potential well Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-28 Shenghao Feng, Jianhua Chen, Jijiang Sun, Xianjiu Huang
In this paper, we consider the following Kirchhoff-Schrödinger-Poisson equation: $$\begin{aligned} \begin{aligned} \left\{ \begin{array}{lc} \left( a+b[u]_s^2\right) (-\varDelta )^s u+V_\lambda (x) u+\phi u=|u|^{p-2}u+|u|^{2_s^*-2} u &{}{} \text { in } {\mathbb {R}}^3, \\ (-\varDelta )^t \phi =u^2 &{}{} \text { in } {\mathbb {R}}^3, \end{array}\right. \end{aligned} \end{aligned}$$ where \(s \in \left(
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On the Fractional Dunkl–Laplacian Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-29 Fethi Bouzeffour, Wissem Jedidi
In this paper, we introduce a novel approach to the fractional Dunkl–Laplacian within a framework derived from specific reflection symmetries in Euclidean spaces. Our primary contributions include pointwise formulas, Bochner subordination, and addressing an extension problem for the fractional Dunkl–Laplacian.
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Time optimal controls for Hilfer fractional evolution equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-21 Yue Liang
This article investigates time optimal controls for the Cauchy problem of Hilfer fractional evolution equations. At first, by employing the fixed point technique and the operator semigroup theory, an existence theorem is obtained. Then the existence of time optimal control pair is studied by applying an approximate technique. An example is given as applications in the last section.
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Multi-parametric Le Roy function revisited Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-16 Sergei Rogosin, Maryna Dubatovskaya
This paper is a continuation of the recent article “Multi-parametric Le Roy function”, Fract. Calc. Appl. Anal. 26(5), 54–69 (2023), https://doi.org/10.1007/s13540-022-00119-y, by S. Rogosin and M. Dubatovskaya. Here we present further analytic properties of the Le Roy function depending on several parameters. Using the Mellin-Barnes representations we determine relations of the multi-parametric Le
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A bifurcation result for a Keller-Segel-type problem Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-16 Giovanni Molica Bisci, Raffaella Servadei, Luca Vilasi
We consider a parametric elliptic problem governed by the spectral Neumann fractional Laplacian on a bounded domain of \(\mathbb {R}^N\), \(N\ge 2\), with a general nonlinearity. This problem is related to the existence of steady states for Keller-Segel systems in which the diffusion of the chemical is nonlocal. By variational arguments we prove the existence of a weak solution as a local minimum of
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Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-07 Linlin Wang, Yuming Xing, Binlin Zhang
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On heat equations associated with fractional harmonic oscillators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-01 Divyang G. Bhimani, Ramesh Manna, Fabio Nicola, Sundaram Thangavelu, S. Ivan Trapasso
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator \(e^{-tH^{\beta }}\), \(t, \beta >0\), associated with the harmonic oscillator \(H=-\Delta + |x|^2\). We then prove some local and global wellposedness results for nonlinear fractional heat equations.
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Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-31 Tinggang Zhao, Changpin Li, Dongxia Li
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Elastic metamaterials with fractional-order resonators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-31 Marcin B. Kaczmarek, S. Hassan HosseinNia
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Approximation results in Sobolev and fractional Sobolev spaces by sampling Kantorovich operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-01 Marco Cantarini, Danilo Costarelli, Gianluca Vinti
The present paper deals with the study of the approximation properties of the well-known sampling Kantorovich (SK) operators in “Sobolev-like settings”. More precisely, a convergence theorem in case of functions belonging to the usual Sobolev spaces for the SK operators has been established. In order to get such a result, suitable Strang-Fix type conditions have been required on the kernel functions
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Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-03 Zhongkai Guo, Xiaoying Han, Junhao Hu
In this paper, the averaging principle for stochastic Caputo fractional differential equations (SCFDEs) with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence
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Spectral analysis of a family of nonsymmetric fractional elliptic operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-31 Quanling Deng, Yulong Li
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Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-30 Binyan Yu, Yongshun Liang
In this paper, we mainly make research on the approximation of continuous functions in the view of the fractal structure based on previous studies. Initially, fractal dimensions and the Hölder continuity of the linear combination of continuous functions have been explored and dense subsets of the space of continuous functions have also been studied. Then, it has been proved that the order of finding
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On the kinetics of $$\psi $$ -fractional differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-27 Weiyuan Ma, Changping Dai, Xin Li, Xionggai Bao
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Generalized fractional Dirac type operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-27 Joel E. Restrepo, Michael Ruzhansky, Durvudkhan Suragan
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy