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This manuscript primarily focuses on the nonlocal controllability results of Hilfer neutral impulsive fractional integro-differential equations of order $ 0\leq w\leq1 $ and $ 0 < g < 1 $ in a Banach space. The outcomes are derived from the strongly continuous operator, Wright function, linear operator, and bounded operator. First, we explore the existence and uniqueness of the results of the mild solution of Hilfer's neutral impulsive fractional integro-differential equations using Schauder's fixed point theorem and an iterative process. In order to determine nonlocal controllability, the Banach fixed point technique is used. We employed some specific numerical computations and applications to examine the effectiveness of the results.

This manuscript primarily focuses on the nonlocal controllability results of Hilfer neutral impulsive fractional integro-differential equations of order 0 ≤ w ≤ 1 and 0 < g < 1 in a Banach space. The outcomes are derived from the strongly continuous operator, Wright function, linear operator, and bounded operator. First, we explore the existence and uniqueness of the results of the mild solution of Hilfer's neutral impulsive fractional integro-differential equations using Schauder's fixed point theorem and an iterative process. In order to determine nonlocal controllability, the Banach fixed point technique is used. We employed some specific numerical computations and applications to examine the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This manuscript mainly focuses on the nonlocal controllability analysis for the impulsive fractional functional integro-differential equation (IFrFIDE) in n-dimensional Euclidean space. To attain the solution representation of the given system, we use the Laplace transform technique and the Mittag-Leffler function. Initially, we obtained the existence and uniqueness of a solution by using the topological degree method, contraction mapping and Gronwall’s inequality. Moreover, we also explore the nonlocal controllability results for our given problem. Furthermore, two numerical examples and a filter system are provided for our given dynamical system. It is helpful to demonstrate the efficacy of our findings.

This manuscript mainly focused on the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. The key ideas of the study are illustrated by using ideas from fractional calculus, the fixed point technique, and measures of noncompactness. Then, the authors establish new criteria for the mild existence of solutions and derive fundamental characteristics of the nonlocal controllability of a system. In addition, researchers offer theoretical and real-world examples to demonstrate the effectiveness and suitability of our suggested solutions. [ABSTRACT FROM AUTHOR]

In this paper, Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions are studied. By using fractional calculus, stochastic analysis, properties of Clarke subdifferential and nonsmooth analysis, sufficient conditions for nonlocal controllability for the considered problem are established. Finally, an example is given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Abstract In this manuscript, we deal with the nonlocal controllability results for the fractional evolution system of 1 < r < 2 $1< r

Abstract In this paper, we consider the nonlocal controllability of α ∈ ( 1 , 2 ) $\alpha\in (1,2)$ -order fractional evolution systems of Sobolev type in abstract spaces. By utilizing fixed point theorems and the theory of resolvent operators we establish some sufficient conditions for the nonlocal controllability of Sobolev-type fractional evolution systems.

Abstract In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . $$ \textstyle\begin{cases} {}^{C} D_{0+}^{\alpha }x(t)=Ax(t)\,dt+ (f(t,x(t))+Bu(t) )\,dg(t), \quad t\in (0, b],\\ x(0)+p(x)=x_{0}. \end{cases} $$ The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.

In this manuscript, we deal with the nonlocal controllability results for the fractional evolution system of 1 < r < 2 in a Banach space. The main results of this article are tested by using fractional calculations, the measure of noncompactness, cosine families, Mainardi's Wright-type function, and fixed point techniques. First, we investigate the controllability results of a mild solution for the fractional evolution system with nonlocal conditions using the Mönch fixed point theorem. Furthermore, we develop the nonlocal controllability results for fractional integrodifferential evolution system by applying the Banach fixed point theorem. Finally, an application is presented for drawing the theory of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlocal controllability of α ∈ (1 , 2) -order fractional evolution systems of Sobolev type in abstract spaces. By utilizing fixed point theorems and the theory of resolvent operators we establish some sufficient conditions for the nonlocal controllability of Sobolev-type fractional evolution systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x (t) = A x (t) d t + (f (t , x (t)) + B u (t)) d g (t) , t ∈ (0 , b ] , x (0) + p (x) = x 0. The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results. [ABSTRACT FROM AUTHOR]

This manuscript mainly focuses on the nonlocal controllability analysis for the impulsive fractional functional integro-differential equation (IFrFIDE) in n-dimensional Euclidean space. To attain the solution representation of the given system, we use the Laplace transform technique and the Mittag-Leffler function. Initially, we obtained the existence and uniqueness of a solution by using the topological degree method, contraction mapping and Gronwall's inequality. Moreover, we also explore the nonlocal controllability results for our given problem. Furthermore, two numerical examples and a filter system are provided for our given dynamical system. It is helpful to demonstrate the efficacy of our findings. • The nonlocal controllability analysis is discussed. • TDM, Gronwall's inequality and the Banach contraction mapping are used. • The application of given dynamical system in the filter model are presented. [ABSTRACT FROM AUTHOR]

In this paper, we establish two sufficient conditions for nonlocal controllability for fractional evolution systems. Since there is no compactness of characteristic solution operators, our theorems guarantee the effectiveness of controllability results under some weakly compactness conditions. [ABSTRACT FROM AUTHOR]