In this article, we study the finite-approximate controllability of a class of non-autonomous semilinear neutral impulsive evolution systems with state-dependent delays in a separable Hilbert space. Our approach is based on constructing a nonlinear solution operator and proving the existence of a fixed point using Schauder’s fixed-point theorem together with the compactness of the associated evolution family. This fixed-point framework is combined with a variational control formulation, which allows us to treat impulses, neutral terms, and memory effects in a unified way under mild assumptions. The resulting criteria guarantee that the system can be steered arbitrarily close to a desired terminal state while matching prescribed finite-dimensional constraints. An application to a semilinear parabolic equation with memory illustrates the effectiveness of the method.

In this article, we introduce the concepts of finite-approximate controllability in the framework of semilinear neutral functional differential equations, focusing on first-order systems within a separable Hilbert space. We establish sufficient conditions for achieving finite-approximate controllability of the semilinear neutral functional differential equation by demonstrating that if the linear part of the system is approximately controllable, then under suitable conditions, the nonlinear part is also finite-approximately controllable. Our approach relies on fixed-point techniques to derive these results. Finally, we provide an example to show the applicability of our theoretical results.

This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the establishment of mild solutions in the semilinear setting. The approach involves constructing a resolvent family for the corresponding integro-differential equation of linear type without memory. The results for the linear system are established first, then extended to the semilinear scenario, followed by a detailed example to illustrate the theoretical findings.

This paper discusses the approximate controllability of a fractional differential control problem driven by a nonlinear hemivariational inequality in a Hilbert space. First, we prove the existence of a mild solution for a fractional control inclusion problem which is equivalent to a hemivariational inequality by using the nonsmooth analysis and fixed point technique. Further, we established sufficient conditions for the approximate controllability of our inclusion problem by taking corresponding linear system is approximately controllable. The existence and controllability results obtained for the inclusion problem are valid for considered nonlinear hemivariational problem. Finally, we provide an example to illustrate the efficiency of the developed results.

This paper investigates the finite-approximate controllability (F-AC) of semilinear impulsive stochastic functional evolution equations in a Hilbert space. First, we establish the existence and uniqueness of a mild solution under suitable conditions. Then, we derive the F-AC results for the considered system. The nonlinear functions adhere to Caratheodory conditions, which offer broader applicability. The Picard iterations, fixed-point principles, and the resolvent-like operator technique are used to derive our results. Finally, an example is presented to validate the abstract theory.

Our motive for this study is to provide some sufficient conditions for the existence of mild solutions and approximate controllability of the semilinear impulsive differential hemivariational inequalities with a general nonlocal condition which is a nonlocal condition modeled in terms of inclusion. After that, we introduce the concept of mild solutions for the corresponding inclusion problem via taking some suitable assumptions. Then we provide a sufficient condition guaranteeing the approximate controllability of our problem and prove by utilizing a fixed-point theorem of multivalued maps and properties of generalized Clarke subdifferential. In this scenario, assuming that the linear system is approximately controllable, we identify three conditions that ensure the approximate controllability of the nonlinear system. Finally, we provide an application to validate our results. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equations with non-instantaneous impulses and finite delay in Hilbert spaces. A set of sufficient conditions of total controllability is obtained for the evolution system under consideration, by imposing the theory of C0-semigroup and Banach fixed point theorem. We also established the total controllability results for a functional integro-differential equation. Finally, an example is given to demonstrate the feasibility of derived abstract results.

This paper examines impulsive controls related to nonautonomous impulsive integro-differential equations in Hilbert space, highlighting their significance. We establish the existence of the mild solution by using fixed point approach and present conditions for approximate controllability using impulsive resolvent operators and the adjoint problem, supported by an illustrative example.

In this manuscript, we study the finite-approximate controllability of impulsive fractional functional evolution equations of order 1<α <2 in Hilbert spaces. We first discuss a useful characterization of the finite-approximate controllability for linear fractional evolution equations of order 1<α <2 in terms of a resolvent-like operator. We also find a suitable control to obtain the approximate controllability of the linear system, which also ensures the finite-approximate controllability of the system. Next, we establish sufficient conditions for the finite-approximate controllability of the semilinear impulsive fractional evolution equations, whenever the corresponding linear system is approximately controllable. Moreover, we provide an example of fractional wave equation to illustrate the efficiency of the developed results. Finally, we discuss the finite-approximate controllability of semilinear fractional evolution equations of order 1<α <2 with finite delay by using a variational method.

This article deals with the approximate controllability problem for fractional evolution equations involving noninstantaneous impulses and state-dependent delay. In order to derive sufficient conditions for the approximate controllability of our problem, we first consider the linear-regulator problem and find the optimal control in the feedback form. By using this optimal control, we develop the approximate controllability of the linear fractional control system. Further, we obtain sufficient conditions for the approximate controllability of the nonlinear problem. In the end, we provide a concrete example to support the applicability of the derived results.

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of second order linear system in detail, which lacks in the existing literature. Then, we derive sufficient conditions for approximate controllability of our system in separable reflexive Banach spaces via linear evolution operator, resolvent operator conditions, and Schauder’s fixed point theorem. Moreover, in this paper, we define proper identification of resolvent operator in Banach spaces. Finally, we provide two concrete examples to validate our results.

In this paper, we consider the second order semilinear impulsive differential equations with state-dependent delay. First, we consider a linear second order system and establish the approximate controllability result by using a feedback control. Then, we obtain sufficient conditions for the approximate controllability of the considered system in a separable, reflexive Banach space via properties of the resolvent operator and Schauder's fixed point theorem. Finally, we apply our results to investigate the approximate controllability of the impulsive wave equation with state-dependent delay.

It is evident that fuzzy arithmetic is different than that of normal arithmetic due to the different classes of functions and symbols. This article is concerned with an appropriate definition of the fractional derivative and integral in a fuzzy sense and a new concept of solutions for a fuzzy Caputo fractional initial value problem (IVP) is presented. Further, under some sufficient conditions on IVP, the existence, uniqueness, and stability results of the solution are established by applying the iterate methods. For the validation of established results, a particular fuzzy fractional Riccati differential equation is presented.

In this paper, impulsive stochastic fractional differential equations (ISFDEs) in Lp (p> 2) space are introduced. We present a general framework for finding solution for ISFDEs. Then, by using the Burkholder - Davis - Gundy inequality and Holder's inequality, we prove the existence and uniqueness of solution to ISFDE by fixed point theorem. We also investigate Lipschitz continuity of solutions with respect to initial values by using Gronwall inequality. Finally, we provide an application to illustrate the results we obtained.

This article deals with the approximate controllability problem for fractional evolution equations involving noninstantaneous impulses and state‐dependent delay. In order to derive sufficient conditions for the approximate controllability of our problem, we first consider the linear‐regulator problem and find the optimal control in the feedback form. By using this optimal control, we develop the approximate controllability of the linear fractional control system. Further, we obtain sufficient conditions for the approximate controllability of the nonlinear problem. In the end, we provide a concrete example to support the applicability of the derived results.

The paper presents a meshfree technique based on the method of fundamental solutions (MFS) and the energy equation associated with the model, to optimize the location of source points. Over the years, the simplest way of distributing the source set has been on a fixed contour lying outside of the considered domain. In this study, a method automates the optimal placement of the source points with the help of the energy conservation equation. The implementation of the scheme is carried forward for the inverse Cauchy problem of heat conduction, and numerical results are provided to establish the new scheme as a superior alternative to MFS.

This manuscript considers a second-order semilinear control system in Hilbert space. By using Tikhonov regularization, we first construct the regularized control for the corresponding linear system and prove its approximate controllability. We then establish approximate controllability results using Gronwall's Lemma for the semilinear system. In addition, the error estimates and convergence rates involved in the regularization procedure are also obtained. Further, we give an example to demonstrate the results.

The current article examines the approximate controllability problem for noninstantaneous impulsive fractional evolution equations of order 1 < α < 2 with statedependent delay in separable reflexive Banach spaces. In order to establish sufficient conditions for the approximate controllability of our problem, we first formulate the linearregulator problem and obtain the optimal control in feedback form. By using this optimal control, we deduce the approximate controllability of the linear fractional control system of order 1 < α < 2. Further, we derive sufficient conditions for the approximate controllability of the nonlinear problem. Finally, we provide a concrete example to validate the efficiency of the derived results .

This study aims to extend, the recently developed, heat polynomial based modified method of fundamental (MFS) solutions to a steady state anisotropic problem. We successfully extend the method to two-dimensional space and test its performance with the help of numerical experiments. Two examples are tested on both convex and nonconvex domains and the results obtained are analyzed. Overcoming the problem of fictitious boundary in standard MFS, modified method in combination with regularization helps us establish that the scheme is accurate, computationally efficient and stable for approximating the solution to this inverse problem, for both exact and noisy data.