Analysis of Ulam-Hyers stability and the existence of solutions in nonlinear Caputo fractional differential equations involving integral boundary conditions
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Abstract
The current study addresses a boundary value problem involving integral boundary conditions with Caputo fractional differential equations and employs the boundary value problem (BVP) framework to establish the existence of solutions via Schaefer's fixed point theorem. Additionally, it leverages contraction mapping principles to prove uniqueness and investigates Ulam-Hyers stability of fractional-order BVPs using Gr\"{o}nwall's inequality. As an illustration, three examples are provided to demonstrate the applicability of our main results.
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References
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