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 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.