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Salim, Abdelkrim; Benchohra, Mouffak; Lazreg, Jamal Eddine; Zhou, Yong

On \(k\)-generalized \(\psi\)-Hilfer impulsive boundary value problem with retarded and advanced arguments in Banach spaces. (English) Zbl 1529.34008

J. Nonlinear Evol. Equ. Appl. 2022, 105-126 (2022).
Summary: This paper deals with the existence and uniqueness results for a class of boundary value problem for implicit nonlinear fractional differential equations with with instantaneous impulses and \(k\)-generalized \(\psi\)-Hilfer fractional derivative involving both retarded and advanced arguments. The result are based on Mönch fixed point theorem associated with the technique of measure of noncompactness. An illustrative example is provided to indicate the applicability of our results.

Cited in 1 Document

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

Keywords:

\(\psi\)-Hilfer fractional derivative; \(k\)-generalized \(\psi\)-Hilfer fractional derivative; impulsions; retarded arguments; Banach space; advanced arguments; existence; uniqueness
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References:

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