Songkran Pleumpreedaporn, Weerawat Sudsutad, Chatthai Thaiprayoon, Sayooj Aby Jose

Qualitative Analysis of Generalized Proportional Fractional Functional Integro-Differential Langevin Equation with Variable Coefficient and Nonlocal Integral Conditions

In this paper, the existence and uniqueness of solutions for a nonlinear generalized proportional fractional functional integro-differential Langevin equation involving variable coefficient via nonlocal multi-point integral conditions are investigated by using Banach's, Schaefer's and Krasnoselskii's fixed point theorems. Different types of Ulam-Hyers stability are also established. Finally, an example is given to demonstrate applicability to the theoretical findings.

Mathematics Subject Classification: 34A08, 34B10, 34B15, 34D20

Key words and phrases: Existence and uniqueness, fixed point theorem, fractional Langevin equation, generalized proportional fractional derivative, nonlocal integral condition, Ulam-Hyers stability