NONLINEAR LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION WITH NONLOCAL MIXED BOUNDARY CONDITIONS INVOLVING A CAPUTO-EXPONENTIAL

NONLINEAR LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION WITH NONLOCAL MIXED BOUNDARY CONDITIONS INVOLVING A CAPUTO-EXPONENTIAL

N. Derdar

[PDF]

Abstract

In this paper, the existence and uniqueness results for a nonlinear Langevin fractional differential equation with nonlocal mixed (multipoint, fractional integral and fractional derivative) boundary conditions involving a Caputo-exponential is studied. The uniqueness result is discussed via Banach’s contraction mapping principle, and the existence of solutions is proved by using Schaefer’s fixed point theorem. Finally, an example is also constructed to demonstrate the application of the main results.

Keywords

Langevin equation, Caputo’s-exponential fractional derivative, implicit fractional differential, nonlocal mixed boundary conditions, fixed point theorems.