Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives

Haq, Abdul

doi:10.1016/j.chaos.2022.111923

Cited by 29 publications

(10 citation statements)

References 36 publications

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“…One can also prove the partial controllability of the same system with or without impulses. For some ideas on partial controllability of the fractional control systems, we refer [48–50].…”

Section: Discussionmentioning

confidence: 99%

Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

Haq,

Sukavanam

2023

Math Methods in App Sciences

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This work studies the controllability of a class of Riemann–Liouville fractional differential equations of order in a new Banach space using fractional cosine family. To derive the existence of solutions, we construct the definition of mild solutions of the system using Laplace transform theory. Then, by assuming the approximate controllability of corresponding linear equation, we prove that the nonlinear dynamical system is approximately controllable using an iterative technique. Lastly, we give an example to illustrate the established theory.

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Section: Discussionmentioning

confidence: 99%

Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

Haq,

Sukavanam

2023

Math Methods in App Sciences

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“…As we all know, calculus was founded by Newton and Leibniz at the second half of the 17th century, and fractional order calculus has gradually become one of the new special fields in natural sciences since 1695. 48 Till now, several types of definitions about the fractional derivative operator and integral operator are discussed and established by many researchers, the classical forms including Riemann-Liouville fractional derivatives, 49 Caputo fractional derivatives, 50 He's fractional derivative, 51 Jumarie fractional derivative, 52 Atangana's fractional derivative, 53 conformable fractional derivative, 54 Abu-Shady-Kaabar fractional derivative, [55][56][57] and the M-fractiona derivative 26,58,59 which will be utilized in this article.…”

Section: Introductionmentioning

confidence: 99%

Abundant explicit solutions for the M-fractional coupled nonlinear Schrödinger–KdV equations

Hong

2023

Journal of Low Frequency Noise, Vibration and Active Control

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In this study, the famous fractional generalized coupled cubic nonlinear Schrödinger–KdV equations arising in many domains of physics and engineering such as depicting the propagation of long waves in dispersive media and the dynamics of short dispersive waves for narrow-bandwidth packet have been investigated. We propose two significant methods named the modified (Gʹ/G, 1/G)-expansion method and the Gʹ/(bGʹ + G + a)-expansion method. After utilizing these two efficient techniques, many types of explicit soliton pulse solutions including the well-known bell-shape bright soliton pulse, the kink and anti-kink dark solitons pulse, the mixed bright-dark soliton pulse, the W-shaped soliton pulse, the periodic waves pulse, and the blow-up soliton pattern solutions are obtained. If we select different values of the frequency, coefficients and orders, the dynamic properties and physical structures of these solutions are discussed, these important results can help us to further understand the inner characteristic of the model.

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“…Various fractional operators have been used. The controllability of semilinear and nonlinear control systems with the Caputo derivative is studied in [3,9,28,35,39], among others, while the Riemann-Liouville derivative is considered in [7,11,12]. Fractional differential equations with the Hilfer derivative have been studied by many authors, see for example [8,10,13,15,24,45,47].…”

Section: Introductionmentioning

confidence: 99%

On the constrained and unconstrained controllability of semilinear Hilfer fractional systems

2023

Archives of Control Sciences

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In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function 𝑓 depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe's fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.

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Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives

Cited by 29 publications

References 36 publications

Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

Abundant explicit solutions for the M-fractional coupled nonlinear Schrödinger–KdV equations

On the constrained and unconstrained controllability of semilinear Hilfer fractional systems

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