On fractional Langevin equation involving two fractional orders in different intervals

Abstract

In this paper, we study a nonlinear Langevin equation involving two fractional orders α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussed.

Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space

“…There is a clear progress on fractional Langevin equations in physics [15][16][17][18][19]. New results on the existence of solutions for fractional Langevin equations under variety of boundary value conditions have been published; see [20][21][22][23][24][25][26][27][28][29] and the references mentioned therein.…”

Positive Solvability for Conjugate Fractional Differential Inclusion of (k, n − k) Type without Continuity and Compactness

“…It is worth mentioning that the literature on the existence and uniqueness of solutions to fractional differential equations is expanding at present, and this problem has drawn the attention of many contributors [19][20][21][22][23][24][25][26][27].…”

A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

“…It is worth remarkable to mention that the field of studying the existence and uniqueness of solutions to fractional differential equations has drawn attention of many contributors [21][22][23][24][25][26][27][28].…”