On $k$-Generalized $\psi$-Hilfer Boundary Value Problems with Retardation and Anticipation

Abstract

In this paper, we prove some existence and uniqueness results for a class of boundary valued problems for implicit nonlinear $k$-generalized $\psi$-Hilfer fractional differential equations involving both retarded and advanced arguments. Further, examples are given to illustrate the viability of our results.

Keywords

• $\psi$-Hilfer fractional derivative
• $k$-generalized $\psi$-Hilfer fractional derivative
• Cauchy-type problem
• retarded arguments
• advanced arguments
• existence
• uniqueness

Kaynakça

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