70 citations · 165 across the 60 of their papers we have counts for
61 papers
Finite-Approximate Solvability of Linear Operator Equations
Nazim I. Mahmudov
We introduce and study the finite-approximate solvability of operator equations \(Lu = h\) in a Hilbert space setting, where a bounded operator \(L \colon U \to H\) is paired with…
Explicit representation of solutions to a linear wave equation with time delay
Javad A. Asadzade, Jasarat J. Gasimov, Nazim I. Mahmudov +1
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded int…
Stochastic Maximum Principles and Linear-Quadratic Optimal Control Problems for Fractional Backward Stochastic Evolution Equations in Hilbert Spaces
Javad A. Asadzade, Nazim I. Mahmudov
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first est…
Representation of solutions to continuous and discrete first-order linear matrix equations with delay
Javad A. Asadzade, Nazim I. Mahmudov
In this paper, we study continuous and discrete linear delay systems given respectively by \[ \dot{X}(ξ) = A_0 X(ξ) + X(ξ)A_1 + B_0 X(ξ-σ) + X(ξ-σ)B_1 + G(ξ), \] and its discrete a…
On the optimality conditions for a fractional diffusive equation with a nonlocal term
Jasarat Gasimov, Nazim Mahmudov
We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order , incorporating a nonlocal time component modeled by an integral kernel.…
On a Diophantine Equation Involving Lucas Numbers
Seyran S. Ibrahimov, Nazim I. Mahmudov
Let L_t denote the t-th Lucas number. We prove that the Diophantine equation L_m^{n+k} + L_m^n = L_r has no solutions in positive integers r, m, n, and k with m >= 2. In the case n…
Explicit solution of second-order delayed discrete equations
Nazim I. Mahmudov
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by…
Remarks on finite-approximate controllability of impulsive evolution systems via resolvent-like operator in Hilbert spaces
Javad A. Asadzade, Nazim I. Mahmudov
In this manuscript, we examine impulsive evolution systems in Hilbert spaces. Using a resolvent-like operator, we first establish the finite-approximate controllability for linear…
Singular mean-field backward stochastic Volterra integral equations in infinite dimensional spaces
Javad A. Asadzade, Nazim I. Mahmudov
This paper investigates the well-posedness of singular mean-field backward stochastic Volterra integral equations (MF-BSVIEs) in infinite-dimensional spaces. We consider the equati…
Approximate controllability of impulsive semilinear evolution equations in Hilbert spaces
Javad A. Asadzade, Nazim I. Mahmudov
Several dynamical systems in fields such as engineering, chemistry, biology, and physics show impulsive behavior by reason of unexpected changes at specific times. These behaviors…
On the Diophantine Equation
Seyran S. Ibrahimov, Nazim I. Mahmudov
In this paper, we examine the Diophantine problem given by the equation , where and . Here, denotes…
Solvability and Optimal Controls of Impulsive Stochastic Evolution Equations in Hilbert Spaces
Javad A. Asadzade, Nazim I. Mahmudov
This paper investigates the solvability and optimal control of a class of impulsive stochastic differential equations (SDEs) within a Hilbert space setting. First, we establish the…
Approximate Controllability of Linear Fractional Impulsive Evolution Equations in Hilbert Spaces
Javad A. Asadzade, Nazim I. Mahmudov
This paper investigates the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. The system under consideration involves the Caputo fra…
Finite Time Stability Analysis for Fractional Stochastic Neutral Delay Differential Equations
Javad A. Asadzade, Nazim I. Mahmudov
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary o…
Second-order maximum principle controlled weakly singular Volterra integral equations
Jasarat J. Gasimov, Nazim I. Mahmudov
This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order…
Necessary first and second order optimality conditions for a fractional order differential equation with state delay
Jasarat J. Gasimov, Nazim I. Mahmudov
In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objectiv…
Discrete delayed perturbation of Mittag-Leffler function and its application to linear fractional delayed difference system
Mustafa Aydin, Nazim I. Mahmudov
The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retard…
Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel
Javad A. Asadzade, Nazim I. Mahmudov
This manuscript examines the problem of nonlinear stochastic fractional neutral integro-differential equations with weakly singular kernels. Our focus is on obtaining precise estim…
A Pillai-Catalan-type problem involving Fibonacci numbers
Seyran S. Ibrahimov, Nazim I. Mahmudov
This paper addresses A Pillai-Catalan-type problem assosiated with Fibonacci numbers. Let be the Fibonacci numbers defined by the recurrence relation , a…
Pontryagin maximum principle for fractional delay differential equations and controlled weakly singular Volterra delay integral equations
Jasarat J. Gasimov, Javad A. Asadzade, Nazim I. Mahmudov
In this article, we explore two distinct issues. Initially, we examine the utilization of the Pontriagin maximum principle in relation to fractional delay differential equations. A…
Delayed Gronwall inequality with weakly singular kernel
Javad A. Asadzade, Jasarat J. Gasimov, Nazim I. Mahmudov
Delay Gronwall inequality with a weakly singular kernel has been a subject of interest in various mathematical studies. In this article, we will delve into the consideration of thi…
Mean-field type discrete stochastic linear quadratic optimal control problems
Arzu Ahmadova, Nazim I. Mahmudov
In this paper, we consider linear quadratic optimal control with mean-field type for discrete-time stochastic systems with state and control dependent noise. An optimal control pro…
Maximum principle for discrete time mean-field stochastic optimal control problems
Arzu Ahmadova, Nazim I. Mahmudov
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of th…
Analytical solution of the fractional linear time-delay systems and their Ulam-Hyers stability
N. I. Mahmudov
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to…