Abstract
In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems, the existence and uniqueness results of solutions are proven. The paper was appended examples which illustrate the applicability of the results.
Highlights
In recent years, the theory of fractional calculus has been developed rapidly
The existence and uniqueness of solutions for boundary value problems of fractional differential equations have been extensively studied [1,2,3,4,5,6,7,8], and an extensive list of references given in that respect
Alongside the intensive development of fractional derivative, the fractional Langevin equations have been introduced by Mainardi and Pironi [10], which was followed by many articles interested with the existence and uniqueness of solutions for fractional Langevin equations [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] and the references given therein
Summary
The existence and uniqueness of solutions for boundary value problems of fractional differential equations have been extensively studied [1,2,3,4,5,6,7,8], and an extensive list of references given in that respect. There are several contributions focusing on the boundary value problems of fractional differential equations, mainly on the existence and uniqueness of the solutions with integrals boundary conditions [3,6]. Inspired by the papers mentioned above, in this paper, we study the existence and uniqueness of solutions for the following boundary value problem of the Langevin equation with two different fractional orders:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
