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).