SOME NEW EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS INVOLVING [psi]-CAPUTO FRACTIONAL DERIVATIVE

This paper concerns the boundary value problem for a fractional differential equation involving a generalized Caputo fractional derivative in b-metric spaces. The used fractional operator is given by the kernel k(t,s) = [psi](t) - [psi](s) and the derivative operator 1/[psi]'(t) d/dt. Some existence results are obtained based on fixed point theorem of [alpha]-[phi]--Graghty contraction type mapping. In the end, we provide some illustrative examples to justify the acquired results. Keywords: [psi]--Caputo fractional derivative, Boundary value problem (BVP), [alpha]-[phi]--Geraghty contractive type mapping, Fixed point (FP). AMS Subject Classification: 83-02, 99A00.