Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

Abstract

In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

Keywords

• boundary value conditions
• caputo’s fractional derivative
• implicit fractional differential equations
• fractional integral
• existence
• stability
• fixed point