13 citations · 21 across the 16 of their papers we have counts for
16 papers
Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity
Arzu Ahmadova, Ismail Huseynov
We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided Hölder regularity. Unlike classical Hölder- or Lipschitz-gradient…
Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds
Ismail Huseynov, Arzu Ahmadova, Agamirza Bashirov
Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous \emph{a posteriori} up…
Partially Exact Controllability of Semilinear Heat Exchanger Systems
Ismail Huseynov, Arzu Ahmadova, Agamirza E. Bashirov
In this paper, we study two semilinear systems describing a monotubular and a two-stream heat exchanger. Neither system is exactly controllable; however, for each we specify a subs…
Design of Optimal Controls in Acausal LQG Problems
Arzu Ahmadova, Agamirza E. Bashirov
In control theory, a system which has output depending only on the present and past values of the input is said to be causal (or nonanticipative). Respectively, a system is acausal…
Convergence results for gradient flow and gradient descent systems in the artificial neural network training
Arzu Ahmadova
The field of artificial neural network (ANN) training has garnered significant attention in recent years, with researchers exploring various mathematical techniques for optimizing…
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…
Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations
Arzu Ahmadova, Nazim Mahmudov
The novelty of our paper is to establish results on asymptotic stability of mild solutions in th moment to Riemann-Liouville fractional stochastic neutral differential equations…
Perturbation of fractional strongly continuous cosine family operators
Ismail T. Huseynov, Arzu Ahmadova, Nazim I. Mahmudov
Perturbation theory has long been a very useful tool in the hands of mathematicians and physicists. The purpose of this paper is to prove some perturbation results for infinitesima…
Some Results on Backward Stochastic Differential Equations of Fractional Order
Nazim I. Mahmudov, Arzu Ahmadova
In this article, we deal with fractional stochastic differential equations, so-called Caputo type fractional backward stochastic differential equations (Caputo fBSDEs, for short),…
Picard approximation of a singular backward stochastic nonlinear Volterra integral equation
Arzu Ahmadova, Nazim I. Mahmudov
Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. In this paper we p…
Perturbation theory for fractional evolution equations in a Banach space
Arzu Ahmadova, Ismail T. Huseynov, Nazim I. Mahmudov
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical proc…
Asymptotic behavior of solutions to fractional stochastic multi-term differential equation systems involving non-permutable matrices
Arzu Ahmadova, Nazim I. Mahmudov
In this paper, we study the exact asymptotic separation rate of two distinct solutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs for short). Our goal in…
A new technique for solving Sobolev type fractional multi-order evolution equations
Nazim I. Mahmudov, Arzu Ahmadova, Ismail T. Huseynov
A strong inspiration for studying Sobolev type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical proces…
Fractional Leibniz integral rules for Riemann-Liouville and Caputo fractional derivatives and their applications
Ismail T. Huseynov, Arzu Ahmadova, Nazim I. Mahmudov
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibni…
Controllability of fractional stochastic delay dynamical systems
Arzu Ahmadova, Ismail T. Huseynov, Nazim I. Mahmudov
In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly…