Existence and Ulam stability results for nonlinear hybrid implicit Caputo fractional differential equations

Abstract

In this paper, we study the existence, uniqueness and estimate of solutions for nonlinear hybrid implicit Caputo fractional differential equations by using the contraction mapping principle and the generalization of Gronwall's inequality. After that, we also establish the Ulam stability for the problem at hand. Finally, an example is given to illustrate this work.

Keywords

• implicit fractional differential equations
• caputo fractional derivatives
• fixed point theorems
• existence
• uniqueness
• ulam stability