Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Abstract

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

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].…”

Existence Solution for Coupled System of Langevin Fractional Differential Equations of Caputo Type with Riemann–Stieltjes Integral Boundary Conditions

“…Analytical expressions of the correlation functions were obtained using the two fluctuation-dissipation theorems and fractional calculus approaches. The fractional Langevin equation has been received the attention of many scientists due to its extremely useful applications in different fields of science and has been dealt with under different conditions (see [8][9][10][11][12][13][14]).…”