Existence results for a generalized fractional boundary value problem in $b$-metric space

Abstract

This paper is concerned with a class of nonlinear boundary value problem involving fractional derivative in the $\phi$-Riemann-Liouville sense. Some Properties of the Green's function for this problem are mentioned. By means of the Banach contraction principle in $b$-metric space and the technique of the $\gamma$-$\psi$- Geraghty contractive maps, existence and uniqueness results are obtained. Two examples are given to support the theoretical results.

12 pages

References in corpus (1)

• A Caputo fractional derivative of a function with respect to another function