Browsing by Author "Mahmudov, Nazim I."

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Delayed Fractional Discrete Sine and Cosine Matrix Functions and Their Applications to Linear Fractional Delayed Difference Oscillating Systems
(Rocky Mt. Math Consortium, 2025) Aydin, Mustafa; Mahmudov, Nazim I.
The fractional discrete retarded cosine and sine matrix functions are defined for the first time in the current paper, and some of their relations are discussed. The variation of constants technique is exploited to obtain an exact analytical form of a general solution to the Cauchy type problem for the linear Riemann-Liouville fractional discrete retarded difference system of order 1 < 2 alpha <= 2 with the noncommutative coefficient matrices. Novel special cases are theoretically presented. In addition, numerical and simulated examples are given to illustrate all of the obtained results.
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.
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.