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

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

Pages : 93-101

Doi:10.32323/ujma.1409291

View : 34 | Download : 49

Publication Date : 2024-05-23

Article Type : Research

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