Existence, uniqueness and Ulam-type stability fornonlocal Caputo fractional boundary value problems
DOI:
https://doi.org/10.66147/lnaa.20264282Keywords:
Caputo derivative, Riemann–Liouville fractional integral, integral solution, nonlocal boundary condition, fixed point method, Ulam-type stabilityAbstract
In this paper, we study a class of nonlocal boundary value problems for Caputo fractional differential equations with integral boundary conditions and Riemann–Liouville memory effects. The equation involves lower-order terms, a nonlinear perturbation, and an internal memory term, while the boundary condition is given by an integral functional. We first derive an equivalent integral formulation and define the corresponding fixed point operator in a suitable function space. Using fractional integral estimates, Krasnoselskii’s fixed point theorem, and Banach’s contraction principle, we establish existence and uniqueness results for integral solutions. The resulting criteria explicitly describe the influence of the Riemann–Liouville memory term on the solvability conditions. We further prove Ulam–Hyers and Ulam–Hyers–Rassias type stability and obtain explicit stability bounds.
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