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In our article, we are primarily concentrating on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential inclusions of order 1 < r < 2. By applying the results and ideas belongs to the cosine function of operators, fractional calculus and fixed point approach, the main results are established. Initially, we establish the approximate controllability of the considered fractional system, then continue to examine the system with the concept of nonlocal conditions. In the end, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

In our article, we are primarily concentrating on existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2. By applying the results and facts belongs to the cosine function of operators, fractional calculus, the measure of noncompactness and fixed point approach, the main results are established. Initially, we focus the existence of mild solution, and later we establish the controllability of the considered fractional system. Finally, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

In our article, we primarily concentrate on the approximate controllability results for Sobolev type fractional stochastic evolution hemivariational inequalities. By applying the facts related to fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system. In the end, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

This manuscript investigates the issue of existence results for fractional differential evolution inclusions of order r ∈ (1, 2) in the Banach space. In the beginning, we analyze the existence results by referring to the fractional calculations, cosine families, multivalued function, and Martelli's fixed point theorem. The result is also used to investigate the existence of nonlocal fractional evolution inclusions of order r ∈ (1, 2). Finally, a concrete application is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

The main motivation of our conversation is the existence and approximate controllability for fractional stochastic Volterra–Fredholm integro-differential systems having order 1 < r < 2. The primary outcomes are obtained by applying concepts and ideas from fractional calculus, multivalued maps, the theory of cosine family, Martelli and Dhage, and Leray–Schauder fixed point techniques. We begin by emphasizing the existence, and then demonstrate the approximate controllability of the considered system. Additionally, we determine the approximate controllability outcomes for the system with infinite delay. At last, an application is established for drawing the theoretical conclusions of primary outcomes. [ABSTRACT FROM AUTHOR]

This research investigates the existence of nonlocal impulsive fractional integrodifferential equations of order 1 < r < 2 with infinite delay. To begin with, we discuss the existence of a mild solution for the fractional derivatives by using the sectorial operators, the nonlinear alternative of the Leray-Schauder fixed point theorem, mixed Volterra-Fredholm integrodifferential types, and impulsive systems. Furthermore, we develop the optimal control results for the given system. The application of our findings is demonstrated with the help of an example. [ABSTRACT FROM AUTHOR]

This manuscript concerns the approximate controllability results in Hilbert space of Hilfer fractional differential inclusions. We show that the Hilfer fractional neutral differential inclusions are approximately controllable using Bohnenblust-Karlin's fixed point theorem. Further, nonlocal conditions are extended to the existence results. Furthermore, an application is shown to demonstrate the theoretical conclusions utility. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and approximate controllability outcomes for Hilfer fractional neutral evolution equations. To begin, we explore existence outcomes using fractional computations and Banach contraction fixed point theorem. In addition, we illustrate that a neutral system with a time delay exists. Further, we prove the considered fractional time-delay system is approximately controllable using the sequence approach. Finally, an illustration of our main findings is offered. [ABSTRACT FROM AUTHOR]

The main focus of this paper is on the boundary controllability of fractional order Sobolevtype neutral evolution equations in Banach space. We show our key results using facts from fractional calculus, semigroup theory, and the fixed point method. Finally, we give an example to illustrate the theory we have established. [ABSTRACT FROM AUTHOR]

In this article, we determine a set of appropriate conditions for approximate controllability of second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay. We verify the main results by applying ideas about the cosine function, sine functions, and fixed point approach. Next, we continue the discussion to the nonlocal second‐order Sobolev‐type differential system. In the end, we provide a theoretical application to assist in the effectiveness of our discussion. [ABSTRACT FROM AUTHOR]

In this manuscript, we are mainly focusing on the existence of mild solutions for the Hilfer fractional evolution system with infinite delay via measures of noncompactness. Fractional calculus and fixed‐point approach are taken into consideration to study the primary outcomes. Finally, we extend the results to the existence of a neutral system with nonlocal conditions. Ultimately, a model is presented for illustration of theory. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of mild solution of functional integrodifferential equation with nonlocal conditions. To establish this results by using the resolvent operator theory and Sadovskii‐Krasnosel'skii type of fixed point theorem and to show the usefulness and the applicability of our results to a broad class of functional integrodifferential equations, an example is given to illustrate the theory. [ABSTRACT FROM AUTHOR]

The study of approximate controllability results ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence and approximate controllability an Atangana-Baleanu-Caputo (ABC)-fractional order neutral delay integrodifferential stochastic systems with nonlocal conditions. For this purpose, the suggested ABC-fractional order neutral integrodifferential stochastic system is transferred into an equivalent fixed point problem via an integral operator. The operator is then analyzed for boundedness, continuity and equicontinuity. Then Arzela-Ascolli theorem ensures the compact multivalued function of the operator and Martelli's fixed point theorem is utilized for the existence of the mild solution. Based on the fixed point theorem and Dunford-Pettis theorem joined with ζ -resolvent operators, we develop the approximate controllability results. Finally, an example is given to justify the theoretical results. The achieved results reveal that the proposed method is systematic and suitable for dealing with the stochastic fractional problems arising in physics, technology, and engineering in terms of the ABC fractional derivative. [ABSTRACT FROM AUTHOR]

In this article, we use the tool of monotone nonlinearity to present the approximate controllability discussion for fractional semilinear system with nonlocal conditions. Monotonicity is an important characteristic in many communications applications in which digital-to-analog converter circuits are used. Such applications can function in the presence of nonlinearity, but not in the presence of non-monotonicity. Therefore, it becomes quite interesting to study a problem assuming monotonicity of the nonlinear function. Also, nonlocal conditions are additional specifications for the physical measurements than classical ones and impart a finer effect on the solution. We formulate the control function for the problem and establish the controllability results. At last, we proposed two applications for the demonstration. [ABSTRACT FROM AUTHOR]

This article is primarily targeting the approximate controllability results of Atangana–Baleanu neutral fractional stochastic hemivariational inequality. The primary conclusions were validated using principles and ideas from stochastic analysis, fractional calculus, multivalued map theory, and fixed point techniques. We begin by emphasizing the existence of mild solutions, and then demonstrate the fractional control system's approximate controllability. Our findings are then applied to the notion of nonlocal circumstances. At last, an example is included to show the applicability of our results. • The Atangana–Baleanu neutral fractional stochastic hemivariational inequality is considered. • Stochastic analysis, multivalued map theory, and fixed point techniques are used. • The existence of mild solutions and approximate controllability are emphasized. [ABSTRACT FROM AUTHOR]

This manuscript mainly focuses on the exact controllability of Sobolev-type Hilfer fractional neutral delay Volterra-Fredholm integro-differential systems. The principal findings of this discussion are established by using the theories on fractional calculus, the measure of noncompactness and Mönch fixed point technique. Initially, the exact controllability of the system is presented and then we improve the discussion to the system with nonlocal conditions. Finally, abstract and filter systems are provided for the illustration. [ABSTRACT FROM AUTHOR]

In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel'skii type of fixed point theorem, a measure of noncompactness and resolvent operator theory. For this work, we have introduced some sufficient conditions to confirm the existence of the neutral partial integrodifferential system. An illustration of the derived results is offered at the end with a filter system corresponding to our existence result. [ABSTRACT FROM AUTHOR]