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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Article number127
JournalJournal of Inequalities and Applications
Volume2023
Issue number1
DOIs
Publication statusPublished - 2023
Externally publishedYes

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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