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.
Highlights
The property of a mathematical object to remain unchanged after an operation or a transformation is called invariance
The reflection principle is invariably presented as a consequence of the strong Markov property
Brownian motion sample paths satisfy the Markov property, symmetry, reflection principle, invariance scaling, time inversion [2,3], and new symmetry nominated as the quasi-time-reversal invariance [4]
Summary
The property of a mathematical object to remain unchanged after an operation or a transformation is called invariance. The close connection between Langevin equations, Brownian motion, and the symmetry principles, observed through the previous discussion, encourages any author to study these equations, their solutions, and the properties of their solutions in various fields. In this investigation, we address the fraction Langevin coupled system of fractional Caputo type. An example showing our results is attached in the final section
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