Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

Boutiara, Abdelatif; Matar, Mohammed M.; Kaabar, Mohammed K. A.; Martínez, Francisco; Etemad, Sina; Rezapour, Shahram

doi:10.1155/2021/9993177

Cited by 16 publications

(7 citation statements)

References 36 publications

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“…Many authors have solved the delay differential equations of fractional order using different approaches. For more details, we refer to [27][28][29][30][31].…”

Section: Application: Solution Of Delay Fractional Differential Equat...mentioning

confidence: 99%

Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

2022

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The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme.

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“…Many authors have solved the delay differential equations of fractional order using different approaches. For more details, we refer to [27][28][29][30][31].…”

Section: Application: Solution Of Delay Fractional Differential Equat...mentioning

confidence: 99%

Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

2022

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“…This approach combines the Mohand transform with the homotopy perturbation method (HPTM). A novel class of neutral FDDEs using the generalized ψ-Caputo derivative on a partially ordered Banach space is investigated by the authors of the study [18]. The Dhage approach and the Banach contraction standard are used to demonstrate the presence and uniqueness of the solutions to the specified boundary value issue.…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Moltot

Deresse

2022

Advances in Mathematical Physics

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In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.

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“…Analytical solutions for the VOFDEs are difficult to obtain because the kernel of the VO's operator has a variable exponent, hence, there will be increasingly rapid developments in numerical approaches to VOFDEs [26][27][28][29]. The delay, neutral delay FDEs, and fractional integro-differential equations (FIDEs) are considered as a generalization and development of FDEs, and dealing with them analytically in most of the cases is difficult [30][31][32][33][34]. The VO fractional delay differential equations (VOFDDEs) are a kind of generalization for the fractional delay differential equations (FDDEs) [35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order

Raslan

Ali

Mohamed

et al. 2022

Journal of Function Spaces

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In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) of variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) of the first kind with the spectral collocation method. The proposed VO-LFDIDEs have multiterms of integer, fractional-order derivatives for delayed or nondelayed and mixed Volterra-Fredholm integral terms. The introduced model is a more general form of linear fractional VO pantograph, neutral, and mixed Fredholm–Volterra integro-differential equations with delay arguments. Caputo’s VO fractional derivative operator is used to generate the matrices of the derivative. Operational matrices are presented for all terms. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. Also, some examples are included to improve the validity and applicability of the techniques. Finally, comparisons between the proposed method and other methods were used to solve this kind of equation.

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Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

Cited by 16 publications

References 36 publications

Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order

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