Nonlocal boundary value problems for integro-differential Langevin equation via the generalized Caputo proportional fractional derivative

Abstract

Abstract Results reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions. The main theorems are proved with the help of Banach’s, Krasnoselskii’s, and Schaefer’s fixed point theorems and Ulam’s approach. Finally, an example is given to demonstrate the applicability of our theoretical findings.

Keywords

• Fractional Langevin equation
• Generalized proportional fractional derivative
• Ulam stability
• Existence and uniqueness
• Nonlocal integral conditions