Approximation of fixed point and its application to fractional differential equation

Khatoon, Sabiya; Uddin, Izhar; Băleanu, Dumitru

doi:10.1007/s12190-020-01445-1

Cited by 23 publications

(9 citation statements)

References 24 publications

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“…Many researchers have studied this topic because it has many applications. Related to this matter, we suggest the recent literature [29][30][31][32][33][34][35] and the references therein.…”

Section: Application To Nonlinear Fractional Differential Equationmentioning

confidence: 94%

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Hussain¹,

Alsulami²,

Alamri³

2023

Computer Modeling in Engineering &Amp; Sciences

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In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with S λ and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results.

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Section: Application To Nonlinear Fractional Differential Equationmentioning

confidence: 94%

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Hussain¹,

Alsulami²,

Alamri³

2023

Computer Modeling in Engineering &Amp; Sciences

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“…A genetic algorithm is an efficient global search method. It has certain robustness, randomness, and implicit parallelism [7]. This algorithm can effectively realize the global optimization search.…”

Section: Improved Technology Of Association Miningmentioning

confidence: 99%

Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data

Jian-jie

dmour

2023

Applied Mathematics and Nonlinear Sciences

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We use the Legendre wavelet method to study nonlinear fractional differential equations. Based on the in-depth study of the characteristics of various fractional-order dynamic system models, this paper designs a system for solving fractional-order differential equations, and we apply them to the anomaly analysis of big computer data. This method can improve the efficiency of big data classification. The results of computer numerical simulation show that the designed algorithm for solving fractional differential equations has high accuracy. At the same time, the algorithm can avoid misclassification and omission in big data analysis.

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“…Recently, Thianwan and Yambangwai [7] introduced a new two-step iteration process involving two G-nonexpansive mappings and studied its convergence analysis in a uniformly convex Banach space endowed with a graph. There is vast literature in this direction for more details (see [8][9][10][11][12][13][14][15][16][17][18][19] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Khatoon

Uddin

Ali

et al. 2021

Journal of Function Spaces

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In this work, we study the convergence of a new faster iteration in which two G -nonexpansive mappings are involved in the setting of uniformly convex Banach spaces with a directed graph. Moreover, by constructing a numerical example, we show the fastness of our iteration procedure over other existing iteration procedures in the literature.

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Approximation of fixed point and its application to fractional differential equation

Cited by 23 publications

References 24 publications

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

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Approximation of fixed point and its application to fractional differential equation

Cited by 23 publications

References 24 publications

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data

Common Fixed Points of Two G -Nonexpansive Mappings via a Faster Iteration Procedure

Contact Info

Product

Resources

About

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure