Existence and stability of solution for a nonlinear fractional differential equation. (English) Zbl 1462.34108
Summary: In this paper, we study a nonlinear \(\psi\)-Hilfer fractional integro-differential equation on finite interval \([a, b]\). Sufficient conditions for the existence of solution and stability for the initial value problem are obtained. Firstly, the existence of solution for the equation is proved by using Banach contraction mapping principle. Then the Ulam-Hyers-Rassias stability, Ulam-Hyers stability, Semi-Ulam-Hyers-Rassias stability of the system are discussed.
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 34K30 | Functional-differential equations in abstract spaces |
| 34K27 | Perturbations of functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
nonlinear fractional differential equation; Banach contraction mapping principle; existence and stability of a solutionReferences:
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