Approximate Controllability of Fractional Nonlinear Hybrid Differential Systems via Resolvent Operators

Matar, Mohammed M.

doi:10.1155/2019/8603878

Cited by 13 publications

(6 citation statements)

References 21 publications

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“…Although this idea seems elementary and simple, it involves remarkable effects and outcomes which describe many physical and natural phenomena accurately. For this reason, research into both of the theoretical and practical aspects of boundary value problems has attracted the focus of many mathematicians in international academic institutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A main difference and novelty in this investigation is the application of the concept of variable order operators.…”

Section: Introductionmentioning

confidence: 99%

Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

et al. 2021

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In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established. To do this, we first investigate some aspects of variable order operators of Hadamard type. Then, with the help of the generalized intervals and piecewise constant functions, we convert the variable order Hadamard FBVP to an equivalent standard Hadamard BVP of the fractional constant order. Further, two fixed point theorems due to Schauder and Banach are used and, finally, the Ulam–Hyers–Rassias stability of the given variable order Hadamard FBVP is examined. These results are supported with the aid of a comprehensive example.

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Section: Introductionmentioning

confidence: 99%

Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

et al. 2021

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“…In the last few years, a large number of studies regarding the existence theory for different FDEs have received much attentions from researchers and some examples include [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Since we can model some of applied phenomena in the framework of the fractional coupled systems, a large number of researchers have conducted many research studies on the existence of solution for such a type of systems (for instances, see [19][20][21][22][23]). Stability analysis along with numerical techniques are the most important components of research in this regard.…”

Section: Introductionmentioning

confidence: 99%

H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method

et al. 2021

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This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples.

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“…FDEqs involving hybrid nonlinearity have been gained much attention during the past few years. This class of equations arises from various mathematical and physical phenomena such as three-layer beam, electromagnetic waves, curved beam's deflection with a constant or varying cross-section, and gravity-driven [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

Boutiara

Matar

Kaabar

et al. 2021

Journal of Function Spaces

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In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ -Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.

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Approximate Controllability of Fractional Nonlinear Hybrid Differential Systems via Resolvent Operators

Abstract: We obtain sufficient conditions for the approximate controllability of a fractional nonlinear hybrid differential system. The results are obtained by using resolvent and sectorial operators technique via Dhage fixed point theorem.

Cited by 13 publications

References 21 publications

Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method

Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

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