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Further investigation of stochastic nonlinear Hilfer-fractional integro-differential inclusions using almost sectorial operators

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Abstract

The purpose of this work is to develop a new model of fractional operators called Hilfer-fractional random nonlinear integro-differential equations. In this paradigm, a further discussion is encouraged under almost sectorial operators. The results are supported by fractional calculus, stochastic analysis theory, and Bohnenblust–Karlin’s fixed point theorem for multi-valued mappings. In addition, a mild solution to the model under consideration is presented. Ultimately, an example is provided to support our results.

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Data availibility

The data used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

FC:

Fractional calculus

FP:

Fixed point

RL:

Riemann–Liouville

SDI:

Stochastic differential inclusion

CFD:

Caputo fractional derivative

HFD:

Hilfer fractional derivative

SO:

Sectorial operator

HS:

Hilbert space

NBCC:

Non-empty, bounded, closed and convex

BS:

Banach space

a.e.:

Almost everywhere

USC:

Upper semicontinuous

LDCT:

Lebesgue’s dominated convergent theorem

SAT:

Stochastic analysis theory.

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Authors and Affiliations

  1. Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, 52571, Buraidah, Saudi Arabia

    Hasanen A. Hammad

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohâg, 82524, Egypt

    Hasanen A. Hammad

  3. Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, Sousse, 4000, Tunisia

    Hassen Aydi

  4. China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Hassen Aydi

  5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

    Hassen Aydi

  6. Department of Mathematics, College of Sciences and Art, King Abdulaziz University, Rabigh, Saudi Arabia

    Doha A. Kattan

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  1. Hasanen A. Hammad
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  3. Doha A. Kattan
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Hassen Aydi.

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Hammad, H.A., Aydi, H. & Kattan, D.A. Further investigation of stochastic nonlinear Hilfer-fractional integro-differential inclusions using almost sectorial operators. J. Pseudo-Differ. Oper. Appl. 15, 5 (2024). https://doi.org/10.1007/s11868-023-00577-9

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  • DOI: https://doi.org/10.1007/s11868-023-00577-9

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