Work

On the Existence of (p,q)-Solutions for the Post-Quantum Langevin Equation: A Fixed-Point-Based Approach

Year: 2025

Type: article

Abstract: The two-parameter (p,q)-operators are a new family of operators in calculus that have shown their capabilities in modeling various systems in recent years. Following this path, in this paper, we present a new construction of the Langevin equation using two-parameter (p,q)-Caputo derivatives. For this new Langevin equation, equivalently, we obtain the solution structure as a post-quantum integral equation and then conduct an existence analysis via a fixed-point-based approach. The use of theorems such as the Krasnoselskii and Leray–Schauder fixed-point theorems will guarantee the existence of solutions to this equation, whose uniqueness is later proven by Banach’s contraction principle. Finally, we provide three examples in different structures and validate the results numerically.

Source: Axioms

DOI: 10.3390/axioms14060474

Authors: Mohammed Jasim Mohammed, Ali Ghafarpanah, Sina Etemad, Sotiris K. Ntouyas, Jessada Tariboon