Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping

Haq, Abdul; Sukavanam, N.

doi:10.1016/j.chaos.2020.110043

Cited by 23 publications

(8 citation statements)

References 40 publications

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“…The conception of controllability was first initiated and established by Kalman [13] in 1960, and since then it is the matter of prime importance for the researchers worldwide. The results of existence and controllability for various differential systems of integer and fractional order involving Riemann-Liouville and Caputo derivatives have closely been demonstrated in many artefacts (refer [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]and references therein).…”

Section: Introductionmentioning

confidence: 73%

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Sahijwani¹,

Sukavanam²,

Haq³

2021

Preprint

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The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions in Banach spaces. First, mild solution of the system is constructed and subsequently its existence is proven using Banach's fixed point theorem. Then, results of approximate controllability are established using concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out correction in examples presented in previous articles.

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Section: Introductionmentioning

confidence: 73%

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Sahijwani¹,

Sukavanam²,

Haq³

2021

Preprint

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“…Wen & Zhou [18] discussed complete and approximate controllability of semilinear system for Caputo derivative with control in the nonlinear part. The results of existence and controllability for various differential systems of integral and fractional order involving Riemann-Liouville and Caputo derivatives have closely been demonstrated in many artefacts (refer [3,6,9,17,[19][20][21][22][23][24][25][26][27][28][29][30][31] and references therein). The article [32] discusses about the numerical treatment of fractional heat equation.…”

Section: Introductionmentioning

confidence: 78%

Approximate controllability for systems of fractional nonlinear differential equations involving Riemann-Liouville derivatives

Sahijwani

Sukavanam

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The article objectifies the approximate controllability of fractional nonlinear differential equations having Riemann-Liouville derivatives. First, the existence of solutions is deduced through fixed point approach and then approximate controllability is proved using Cauchy convergence through iterative and approximate techniques. The theory of semigroup together with probability density function has been utilized to reach the desired conclusions.

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“…The existence and controllability results for various types of systems are proved by many researchers 21–52,53–61 . In recent years, the controllability properties of Caputo fractional systems have been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

“…The existence and controllability results for various types of systems are proved by many researchers. [53][54][55][56][57][58][59][60][61] In recent years, the controllability properties of Caputo fractional systems have been extensively studied. However, the work on the controllability of Riemann-Liouville fractional systems is still in the initial phase.…”

Section: Introductionmentioning

confidence: 99%

Existence and controllability of higher‐order nonlinear fractional integrodifferential systems via fractional resolvent

Haq

Sukavanam

2022

Math Methods in App Sciences

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This work analyzes the existence of solution and approximate controllability for higher‐order nonlinear fractional integrodifferential systems with Riemann–Liouville derivatives in Banach spaces. First, the definition of mild solution for the system is derived. Then a set of sufficient conditions for the existence of mild solution and approximate controllability of the system is obtained. The discussions are based on fixed point approach, and the theory of convolution and fractional resolvent. To illustrate the feasibility of developed theory, an example is given.

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Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping

Cited by 23 publications

References 40 publications

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

Approximate controllability for systems of fractional nonlinear differential equations involving Riemann-Liouville derivatives

Existence and controllability of higher‐order nonlinear fractional integrodifferential systems via fractional resolvent

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