Browsing by Author "Mahmudov, Nazim I."

Now showing 1 - 5 of 5

Relative Controllability of Fractional Dynamical Systems With a Delay in State and Multiple Delays in Control
(Wiley, 2025) Aydin, Mustafa; Mahmudov, Nazim I.
This work is devoted to the study of the relative controllability of fractional dynamic systems in finite-dimensional spaces with a state delay and multiple delays in control. For linear systems to be relatively controllable, necessary and sufficient conditions are determined by defining and using the Gramian matrix. The controllability conditions for semilinear systems are determined on the basis of Schauder's fixed point theorem.
Relative Controllability of Langevin Delayed Fractional System with Multiple Delays in Control
(Zhejiang University Press, 2025) Aydin, Mustafa; Mahmudov, Nazim I.
A Langevin delayed fractional system with multiple delays in control, is a delayed fractional system that includes delay parameters in both state and control, is first introduced. This paper is devoted to investigating the relative controllability of the Langevin delayed fractional system with multiple delays in control. For linear systems to be relatively controllable, necessary and sufficient circumstances are identified by introducing and employing the Gramian matrix. The sufficient conditions for the relative controllability of semilinear systems are offered based on Schauder's fixed point theorem. As an unusual approach, the controllability results of the delayed system are built for the first time on the exact solution produced by the Mittag-Leffler type function although controllability ones in the literature are built on the Volterra integral equations or the mild solutions produced by resolvent families.
Representation of Solutions To Tempered Delayed Ψ-Fractional Systems With Noncommutative Coefficients
(Pergamon–Elsevier Science Ltd, 2025) Aydin, Mustafa; Mahmudov, Nazim I.
This paper focuses on deriving explicit solutions for tempered delayed fractional differential systems that utilize Caputo fractional derivatives in relation to another function. To achieve this, we define tempered yr-delayed perturbations of Mittag-Leffler type functions and explore their yr-Laplace transforms. Additionally, we discuss theorems related to shifting and time-delay in the context of yr-Laplace transforms. Utilizing the tempered yr-delayed perturbational function, we establish a representation of explicit solutions for the system through the Laplace transform method. This representation is validated by demonstrating that it satisfies the system, alongside employing the method of variation of constants. Several novel special cases are introduced, and a numerical example is provided to demonstrate the practical application of the results obtained.
Some Applications of the Generalized Laplace Transform and the Representation of a Solution To Sobolev-Type Evolution Equations With the Generalized Caputo Derivative
(Polska Akad Nauk, Polish Acad Sci, Div Iv Technical Sciences Pas, 2024) Aydin, Mustafa; Mahmudov, Nazim I.
We introduce the Sobolev-type multi -term mu-fractional evolution with generalized fractional orders with respect to another function. We make some applications of the generalized Laplace transform. In the sequel, we propose a novel type of Mittag-Leffler function generated by noncommutative linear bounded operators with respect to the given function and give a few of its properties. We look for the mild solution formula of the Sobolev-type evolution equation by building on the aforementioned Mittag-Leffler-type function with the aid of two different approaches. We share new special cases of the obtained findings.
ψ-Caputo Type Time-Delay Langevin Equations With Two General Fractional Orders
(Wiley, 2023) Aydin, Mustafa; Mahmudov, Nazim I.
In the present paper, first, a Psi-delayed Mittag-Leffler type function is introduced, which generalizes the existing delayed Mittag-Leffler type function. Second, by means of Psi-delayed Mittag-Leffler type function, an exact analytical solution formula to non-homogeneous linear delayed Langevin equations involving two distinct Psi-Caputo type fractional derivatives of general orders is obtained. Moreover, existence and uniqueness, stability of solution to nonlinear delayed Langevin fractional differential equations is obtained in the weighted space. Numerical and simulated examples are shared to exemplify the theoretical findings.