Controllability Problem of Fractional Neutral Systems: A Survey

Babiarz, Artur; Niezabitowski, Michał

doi:10.1155/2017/4715861

Cited by 16 publications

(7 citation statements)

References 65 publications

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“…Neutral fractional equations have attracted the interests of many researchers due to the important applications of these equations in physics and engineering, and these equations share some physical characteristics of wave equation due to the physical explanation of these equations as damped waves that have constant propagation velocities [33]. Agarwal et al [34] proved the fractional formulation's existence of neutral differential equations via Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

et al. 2021

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A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

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Section: Introductionmentioning

confidence: 99%

Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

et al. 2021

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“…Fractional calculus has been of increasing interest to scientists and engineers, arising in mathematical physics, chemistry, modeling mechanical and electrical properties of real phenomena [ 1 , 2 , 3 , 4 , 5 , 6 ]. Fractional calculus has been recognized as a powerful instrument to discover the secret directions of various material and physical processes that deal with derivatives and integrals of arbitrary orders [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

Applying Discrete Homotopy Analysis Method for Solving Fractional Partial Differential Equations

Özpinar

2018

Entropy

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Abstract:In this paper we developed a space discrete version of the homotopy analysis method (DHAM) to find the solutions of linear and nonlinear fractional partial differential equations with time derivative α (0 < α ≤ 1). The DHAM contains the auxiliary parameter , which provides a simple way to guarantee the convergence region of solution series. The efficiency and accuracy of the proposed method is demonstrated by test problems with initial conditions. The results obtained are compared with the exact solutions when α = 1. It is shown they are in good agreement with each other.

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“…For further introduction to the concept of controllability with diverse applications, refer to major contributions [1][2][3][4][5][6][7][8][9][10] and related references therein. The concept of controllability with applications in engineering has been studied by many authors, a part of which can be found in [11][12][13][14][15][16] and in related references therein. Results obtained in this paper can be used in relevant applied studies in engineering, e.g., [17][18][19][20], for derivation of diverse control regimes.…”

Section: Introductionmentioning

confidence: 99%

Heuristic Determination of Resolving Controls for Exact and Approximate Controllability of Nonlinear Dynamic Systems

Khurshudyan

2018

Mathematical Problems in Engineering

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Dealing with practical control systems, it is equally important to establish the controllability of the system under study and to find corresponding control functions explicitly. The most challenging problem in this path is the rigorous analysis of the state constraints, which can be especially sophisticated in the case of nonlinear systems. However, some heuristic considerations related to physical, mechanical, or other aspects of the problem may allow coming up with specific hierarchic controls containing a set of free parameters. Such an approach allows reducing the computational complexity of the problem by reducing the nonlinear state constraints to nonlinear algebraic equations with respect to the free parameters. This paper is devoted to heuristic determination of control functions providing exact and approximate controllability of dynamic systems with nonlinear state constraints. Using the recently developed approach based on Green’s function method, the controllability analysis of nonlinear dynamic systems, in general, is reduced to nonlinear integral constraints with respect to the control function. We construct parametric families of control functions having certain physical meanings, which reduce the nonlinear integral constraints to a system of nonlinear algebraic equations. Regimes such as time-harmonic, switching, impulsive, and optimal stopping ones are considered. Two concrete examples arising from engineering help to reveal advantages and drawbacks of the technique.

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Controllability Problem of Fractional Neutral Systems: A Survey

Cited by 16 publications

References 65 publications

Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

Applying Discrete Homotopy Analysis Method for Solving Fractional Partial Differential Equations

Heuristic Determination of Resolving Controls for Exact and Approximate Controllability of Nonlinear Dynamic Systems

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