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

Abstract

By employing Shauder fixed-point theorem, this work tries to obtain the existence results for the solution of a nonlinear Langevin coupled system of fractional order whose nonlinear terms depend on Caputo fractional derivatives. We study this system subject to Stieltjes integral boundary conditions. A numerical example explaining our result is attached.

On Coupled System of Langevin Fractional Problems with Different Orders of μ-Caputo Fractional Derivatives

“…Fractional differential equations (FDEs) have gained a lot of attention in recent years due to their numerous applications in engineering, physics, biology, chemistry, and other fields (see, for instance, [1][2][3][4][5][6], and the references therein for more information on the boundary value issues of FDEs and inclusions subject to diverse boundary conditions). Differential inclusion and differential equations are thought to be particularly helpful when studying dynamical systems and stochastic processes (see [7][8][9][10] for some recent related results).…”

Non-Instantaneous Impulsive BVPs Involving Generalized Liouville–Caputo Derivative

“…Due to the importance of the Caputo version, there are many versions established as generalization of it, such as Caputo-Katugampola, Caputo-Hadamard, Caputo-Fabrizio, etc. Furthermore, it is drown attention of huge number of contributors to study physical and mathematical modelings contain it and its related versions, see [9][10][11][12][13] and references cited therein.…”

Coupled Fixed Point Theorem for the Generalized Langevin Equation with Four-Point and Strip Conditions

“…The Brownian motion exceedingly draws through the Langevin equation when the random fluctuation force is submitted to be white noise. If the random oscillation force is not white noise, the object motion is depicted by the generalized Langevin equation [14]. Overall, the ordinary differential equations cannot precisely characterize experimental data and area measurement; as an alternative approach, fractional-order differential equation models are extremely used today [15][16][17].…”