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

Year 2024, Volume: 7 Issue: 2, 93 - 101, 23.05.2024

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

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

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

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