Discrete fractional Bihari inequality and uniqueness theorem of solutions of nabla fractional difference equations with non-Lipschitz nonlinearities

Wang, Mei; Jia, Baoguo; Chen, Churong; Zhu, Xiaoyan; Du, Feifei

doi:10.1016/j.amc.2020.125118

Cited by 10 publications

(6 citation statements)

References 13 publications

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“…This result cannot be obtained using the currently accessible discrete fractional Gronwall inequality. The study utilized the semi-group approach to examine the accuracy of solutions in Banach space FDEqs of the heat type [7].…”

Section: Introductionmentioning

confidence: 99%

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

Shammaky,

Youssef,

Abdou

et al. 2023

Fractal Fract

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This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed.

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Section: Introductionmentioning

confidence: 99%

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

Shammaky,

Youssef,

Abdou

et al. 2023

Fractal Fract

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“…Compared with traditional integer-order systems, fractional-order systems have more degrees of freedom and infinite memory [1,2]. Because of these advantages, the integration of fractional-order calculus into nonlinear dynamical system has gained attention and resulted in several new developments in this domain [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Global dissipativity and adaptive synchronization for fractional‐order time‐delayed genetic regulatory networks

Zhang

Anbalagan

et al. 2021

Asian Journal of Control

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This manuscript examines global dissipativity and synchronization criteria for time-delayed fractional-order gene regulatory networks (FGRNs). The Lyapunov stability theory is used to examine a class of FGRNs with delay arguments that are inspired by the integer-order delayed gene regulatory network model. Some sufficient criteria are established using the fractional-order comparison principle and stability theorem for fractional-order time-delayed systems to ensure the global dissipativity solution of FGRNs with both feedback regulation and translation time delays. Furthermore, for FGRNs, the global asymptotic synchronization condition is accomplished by constructing an adaptive delayed feedback control method for the master-slave system. Finally, two numerical examples are provided to demonstrate the applicability and superiority of the conclusions obtained.

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“…Recently, surprising achievement has been produced as a result of arduous attempts in fractional difference structures by Du and Jia [10]. The existence and uniqueness of solutions are the foundation for examining the stability problem that has been exploited using fractional Gronwall and Bihari inequality, for example [11,12].…”

Section: Introduction and Essentialsmentioning

confidence: 99%

Discrete Fractional Inequalities Pertaining a Fractional Sum Operator with Some Applications on Time Scales

Khan

Shah

2021

Journal of Function Spaces

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This content replicates some discrete nonlinear fractional inequalities by virtue of the fractional sum operator Ψ ¯ on time scales. Through the recognition of the principle of discrete fractional calculus, we are able to recover the precise estimates for unknown functions of inequalities of the Gronwall type. The resultant inequalities are of unique structure comparative with the latest reviewing disclosures and can be described as a complementary tool for numerically testing the solutions of discrete partial differential equations. The foremost consequences are probably confirmed via handling of assessment procedure and technique of mean value speculation. We display few examples of the proposed inequalities to represent the incentives of our effort.

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Discrete fractional Bihari inequality and uniqueness theorem of solutions of nabla fractional difference equations with non-Lipschitz nonlinearities

Cited by 10 publications

References 13 publications

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

Global dissipativity and adaptive synchronization for fractional‐order time‐delayed genetic regulatory networks

Discrete Fractional Inequalities Pertaining a Fractional Sum Operator with Some Applications on Time Scales

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