On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent

Mokhtar Mokhtari; Ahmed Refice; Mohammed Said Souıd; Ali Yakar

doi:10.32323/ujma.1409291

EN

On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent

Abstract

This paper aims to investigate the existence, uniqueness, and stability properties for a class of fractional weighted Cauchy-type problem in the variable exponent Lebesgue space $L^{p(.)}$. The obtained results are set up by employing generalized intervals and piece-wise constant functions so that the $L^{p(.)}$ is transformed into the classical Lebesgue spaces. Moreover, the usual Banach Contraction Principle is utilized, and the Ulam-Hyers (UH) stability is studied. At the final stage, we provide an example to support the accuracy of the obtained results.

Keywords

Fixed point theorem, Fractional differential equations, Ulam-Hyers stability, Variable exponent Lebesgue spaces

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Mokhtar Mokhtari
0000-0002-2504-5278
Algeria

Ahmed Refice
0000-0002-8906-6211
Algeria

Mohammed Said Souıd
0000-0002-4342-5231
Algeria

Ali Yakar ^*
0000-0003-1160-577X
Türkiye

Early Pub Date

May 16, 2024

Publication Date

May 23, 2024

Submission Date

December 24, 2023

Acceptance Date

May 2, 2024

Published in Issue

Year 2024 Volume: 7 Number: 2

DOI

https://doi.org/10.32323/ujma.1409291

IZ

https://izlik.org/JA32JU93CC

APA

Mokhtari, M., Refice, A., Souıd, M. S., & Yakar, A. (2024). On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent. Universal Journal of Mathematics and Applications, 7(2), 93-101. https://doi.org/10.32323/ujma.1409291

AMA

1.Mokhtari M, Refice A, Souıd MS, Yakar A. On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent. Univ. J. Math. Appl. 2024;7(2):93-101. doi:10.32323/ujma.1409291

Chicago

Mokhtari, Mokhtar, Ahmed Refice, Mohammed Said Souıd, and Ali Yakar. 2024. “On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces With Variable Exponent”. Universal Journal of Mathematics and Applications 7 (2): 93-101. https://doi.org/10.32323/ujma.1409291.

EndNote

Mokhtari M, Refice A, Souıd MS, Yakar A (May 1, 2024) On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent. Universal Journal of Mathematics and Applications 7 2 93–101.

IEEE

[1]M. Mokhtari, A. Refice, M. S. Souıd, and A. Yakar, “On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent”, Univ. J. Math. Appl., vol. 7, no. 2, pp. 93–101, May 2024, doi: 10.32323/ujma.1409291.

ISNAD

Mokhtari, Mokhtar - Refice, Ahmed - Souıd, Mohammed Said - Yakar, Ali. “On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces With Variable Exponent”. Universal Journal of Mathematics and Applications 7/2 (May 1, 2024): 93-101. https://doi.org/10.32323/ujma.1409291.

JAMA

1.Mokhtari M, Refice A, Souıd MS, Yakar A. On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent. Univ. J. Math. Appl. 2024;7:93–101.

MLA

Mokhtari, Mokhtar, et al. “On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces With Variable Exponent”. Universal Journal of Mathematics and Applications, vol. 7, no. 2, May 2024, pp. 93-101, doi:10.32323/ujma.1409291.

Vancouver

1.Mokhtar Mokhtari, Ahmed Refice, Mohammed Said Souıd, Ali Yakar. On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent. Univ. J. Math. Appl. 2024 May 1;7(2):93-101. doi:10.32323/ujma.1409291