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Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order

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2023

Authors

Benia, Kheireddine
Souid, Mohammed Said
Jarad, Fahd
Alqudah, Manar A.
Abdeljawad, Thabet

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Abstract

This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam–Hyers–Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results. © 2023, Springer Nature Switzerland AG.

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Keywords

Boundary Value Problem, Derivatives and Integrals of Variable Order, Fixed Point Theorem, Measure of Non-Compactness, Weighted Fractional Integrals, Weighted Spaces of Summable Functions

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Benia, Kheireddine...et al. (2023). "Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order", Journal of Inequalities and Applications, Vol. 2023, No. 1.

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Journal of Inequalities and Applications

Volume

2023

Issue

1

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