## SOME NEW EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS INVOLVING ????-CAPUTO FRACTIONAL DERIVATIVE

## SOME NEW EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS INVOLVING ????-CAPUTO FRACTIONAL DERIVATIVE

*H. Afshari, M. S. Abdo, M. N. Sahlan*

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## Abstract

This paper concerns the boundary value problem for a fractional di erential equation involving a generalized Caputo fractional derivative in bmetric spaces. The used fractional operator is given by the kernel k(t; s) = (t) (s) and the derivative operator 1 0(t) d dt . Some existence results are obtained based on xed point theorem of - Graghty contraction type mapping. In the end, we provide some illustrative exam- ples to justify the acquired results.

## Keywords

Caputo fractional derivative, Boundary value problem (BVP), { ????Geraghty contractive type mapping, Fixed point (FP).