Browsing by Author "Mahmudov, N. I."

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Qualitative Analysis of the Prabhakar-Caputo Type Fractional Delayed Equations
(Inst Applied Mathematics, 2025) Aydin, M.; Mahmudov, N. I.
The representation of an explicit solution to the Prabhakar fractional differential delayed system is studied employing the far-famed Laplace transform technique. Second, the existence uniqueness of the solution is debated together with the Ulam-Hyers stability of a semilinear Prabhakar fractional differential delayed system. Thirdly, the necessary and sufficient circumstances for the controllability of linear Prabhakar fractional differential delayed system are determined by describing the Gramian matrix. A sufficient circumstance for the relative controllability of a semilinear Prabhakar fractional differential delayed system is studied via the Krasnoselskii's fixed point theorem. Numerical examples are offered to verify the theoretical findings.
The Sequential Conformable Langevin-Type Differential Equations and Their Applications To the Rlc Electric Circuit Problems
(Hindawi Ltd, 2024) Aydin, M.; Mahmudov, N. I.
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.
A Study on Linear Prabhakar Fractional Systems With Variable Coefficients
(Springer Basel Ag, 2024) Aydin, Mustafa; Mahmudov, N. I.
The focus of this paper is on addressing the initial value problem related to linear systems of fractional differential equations characterized by variable coefficients, incorporating Prabhakar fractional derivatives of Riemann-Liouville and Caputo types. Utilizing the generalized Peano-Baker series technique, the state-transition matrix is acquired. The paper presents closed form solutions for both homogeneous and inhomogeneous cases, substantiated by illustrative examples.