Existence and stability of solution for nonlinear differential equations with \(\psi \)-Hilfer fractional derivative. (English) Zbl 1476.45010
Summary: In this paper, we investigate a nonlinear \(\psi \)-Hilfer fractional integro-differential equation on an unbounded domain \([ a , + \infty )\). Firstly, the existence and uniqueness of solution for the equation are proved by means of Banach contraction mapping principle based on suitable growth conditions in an appropriate Banach space. Moreover the stability of Ulam-Hyers-Rassias, Ulam-Hyers and Semi-Ulam-Hyers-Rassias to the initial value problem is obtained.
MSC:
| 45M10 | Stability theory for integral equations |
| 26A33 | Fractional derivatives and integrals |
| 34A08 | Fractional ordinary differential equations |
Keywords:
nonlinear differential equation; \( \psi \)-Hilfer fractional derivative; Banach contraction mapping principleReferences:
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