Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator

Hyder, Abd‐Allah; El-Badawy, M.

doi:10.1155/2019/1389787

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…Moreover, the optimality conditions are derived. In [19], the distributed control for a time-fractional differential system involving a Schrödinger operator is studied, and the optimality conditions are derived. Furthermore, space-fractional optimal control is introduced.…”

Section: R N Y(x)y(t)mentioning

confidence: 99%

Optimal control for cooperative systems involving fractional Laplace operators

2021

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In this work, the elliptic $2\times 2$ 2 × 2 cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.

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Section: R N Y(x)y(t)mentioning

confidence: 99%

Optimal control for cooperative systems involving fractional Laplace operators

2021

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“…Te signifcance of this study may be seen in numerous technological and physical uses where these derivatives can more accurately represent them in the scientifc domains. Also, the fractional application models can give a more precise understanding of the difculties in the real world [12][13][14][15][16]. Below are some fractional calculus principles that will be exploited throughout this study.…”

Section: Introductionmentioning

confidence: 99%

New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals

Hyder

2023

Journal of Mathematics

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In most fields of applied sciences, inequalities are important in constructing mathematical systems and associated solution functions. Convexity also has a significant impact on an assortment of mathematical topics. By utilizing a comprehensive version of Riemann–Liouville integrals and the functions’ convexity condition, we present and prove novel fractional inequalities. According to the current literature, this work is a novel addition to the literature, and the proposed technique for addressing fractional inequalities issues is straightforward and simple to execute. It is also easy to see that all of the inequalities that have been developed are inclusive and may be reduced to a variety of other inequalities that have been proposed in the literature. Additionally, certain numeric examples with graphs are provided to support the theoretical results.

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“…It is viewed as a powerful and efficacious tool for modelling linear and nonlinear systems. There are many physical and mathematical applications of the GC and pertinent non-integer order transforms such as electrical circuits, control theory, dynamics of stock markets, dynamics of viscoelastic materials, modelling of diffusion, thermoelasticity, fluid mechanics, stochastic processes, fractional dynamics, signal processing and so on [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A new generalized θ-conformable calculus and its applications in mathematical physics

Hyder

Soliman

2020

Phys. Scr.

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In this work, a new generalized concept of conformable derivative is given and named generalized θ–conformable derivative (GTCD). Several properties are studied such as the chain rule, the quotient rule, the product rule, the Rolle’s theorem, the mean value theorem and the fundamental theorems of calculus. Also, the geometrical and physical interpretations of the GTCD are presented. It is very easy to see that the GTCD is comprehensive and includes many past derivatives as special cases. An application of the generalized θ–conformable derivatives (GTCDs) is presented along with the G ′ / G , 1 / G –approach to construct a novel gathering of exact solutions for the nonlinear (2+1)-dimensional biological population model (BPM) involving GTCDs. Moreover, some comparisons and graphical interpretations are given to support our results related to the (2+1)-dimensional BPM. All acquired results regarding the GTCD show its validity to applying in many problems in mathematical physics, engineering, biology and others.

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Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator

Cited by 6 publications

References 21 publications

Optimal control for cooperative systems involving fractional Laplace operators

Optimal control for cooperative systems involving fractional Laplace operators

New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals

A new generalized θ-conformable calculus and its applications in mathematical physics

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