The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems

Abstract

In this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms' technique. Also, existence and uniqueness of a global solution to its nonlinear version are obtained. The existence and uniqueness of solutions are shown with respect to the weighted norm defined in compliance with (conformable) exponential function. The concept of the Ulam-Hyers stability of solutions is debated based on the fixed-point approach. The LRC electrical circuits are presented as an application to the described system. Simulated and numerical instances are offered to instantiate our abstract findings.