Benia, KheireddineSouid, Mohammed SaidJarad, FahdAlqudah, Manar A.Abdeljawad, Thabet2024-05-292024-05-292023Benia, 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. 1.1025-5834http://hdl.handle.net/20.500.12416/8428This 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.eninfo:eu-repo/semantics/openAccessBoundary Value ProblemDerivatives and Integrals of Variable OrderFixed Point TheoremMeasure of Non-CompactnessWeighted Fractional IntegralsWeighted Spaces of Summable FunctionsArticle2023110.1186/s13660-023-03042-9