An Analytical Study of Variable-Coefficient Boundary Value Problems With Generalized Tempered Fractional Operators

Jabr Aljedani

Journal of Mathematics, 2026, vol. 2026, 1-13

Abstract: In this paper, we investigate a class of nonlinear tempered fractional boundary value problems (BVPs) with a generalized Caputo-type derivative with respect to a kernel function. The problem includes variable coefficients, a nonlinear term depending on lower-order derivatives, a tempered fractional integral term, and a nonlocal multipoint integral boundary condition. We transform the fractional BVP to an equivalent integral equation and then form the corresponding fixed point operator in a suitable Banach space. Schauder’s fixed-point theorem with a growth condition and uniqueness is obtained by Banach’s contraction principle with a Lipschitz condition. Also, the Ulam–Hyers (U–H) and Ulam–Hyers–Rassias (U–H–R) stabilities are investigated. Finally, two examples are given to illustrate the applicability of the theoretical results.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5530865

DOI: 10.1155/jom/5530865

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