Existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations

Abstract

In this paper, we use the contraction mapping principle to obtain the existence, interval of existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations. We also use the generalization of Gronwall’s inequality to show the estimate of the solutions.

Keywords

• implicit fractional differential equations
• caputo-hadamard fractional derivatives
• fixed point theorems
• existence uniqueness