Existence, uniqueness and regularity of solutions for fractional integro-differential equations with state-dependent delay. (English) Zbl 07923009
Summary: Within this paper, we consider the existence and uniqueness of solutions for fractional integro-differential equations with state-dependent delay on the Lipschitz continuous function space. Our results are obtained by using the resolvent operator theory and the generalized Banach contraction mapping principle. The regularity of solutions of fractional integro-differential equations with state-dependent delay is also discussed. Finally, an example is provided as an application.
MSC:
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34K05 | General theory of functional-differential equations |
| 45K05 | Integro-partial differential equations |
| 47A10 | Spectrum, resolvent |
Keywords:
fractional integro-differential equations; state-dependent delay; resolvent theory; generalized Banach contraction mapping principleReferences:
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