Analysis of a New Fractional Model for Damped Bergers’ Equation

AbstractIn this article, we present a fractional model of the damped Bergers’ equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.

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Analysis of a fractional tumor-immune interaction model with exponential kernel

Filomat ◽

10.2298/fil2106023d ◽

2021 ◽

Vol 35 (6) ◽

pp. 2023-2042

Author(s):

Mustafa Dokuyucu ◽

Hemen Dutta

Keyword(s):

Fixed Point ◽

Fractional Derivative ◽

Numerical Solution ◽

Interaction Model ◽

Existence Of Solution ◽

Fixed Point Method ◽

Ulam Stability ◽

Derivative Operator ◽

Exponential Kernel ◽

The Stability

In this paper, a tumor-immune interaction model has been analyzed via Caputo-Fabrizio fractional derivative operator with exponential kernel. Existence of solution of the model has been established with a fixed-point method and then it demonstrated the uniqueness of solution also. The stability of the model has been analyzed with the help of Hyers-Ulam stability approach and then numerical solution by using the Adam-Basford method. The results are further examined in detail with simulations for different fractional derivative values.

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Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0307 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Mohamed M. Khader

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Numerical Solution ◽

Numerical Results ◽

Convergence Order ◽

Variable Order ◽

Numerical Treatment ◽

Dynamical Models ◽

Fractional Modeling ◽

Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

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Modified Kawahara equation within a fractional derivative with non-singular kernel

Thermal Science ◽

10.2298/tsci160826008k ◽

2018 ◽

Vol 22 (2) ◽

pp. 789-796 ◽

Cited By ~ 26

Author(s):

Devendra Kumar ◽

Jagdev Singh ◽

Dumitru Baleanu

Keyword(s):

Fractional Derivative ◽

Numerical Solution ◽

Water Waves ◽

Iterative Scheme ◽

Singular Kernel ◽

Kawahara Equation ◽

Long Wavelength ◽

Exponential Kernel ◽

The Stability ◽

Linear Water Waves

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

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Solving Volterra Integrodifferential Equations via Diagonally Implicit Multistep Block Method

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2018/7392452 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Nur Auni Baharum ◽

Zanariah Abdul Majid ◽

Norazak Senu

Keyword(s):

Stability Analysis ◽

Numerical Solution ◽

Numerical Method ◽

Numerical Computation ◽

Numerical Solutions ◽

Numerical Results ◽

Integrodifferential Equations ◽

Block Method ◽

The Stability ◽

Predictor Corrector

The performance of the numerical computation based on the diagonally implicit multistep block method for solving Volterra integrodifferential equations (VIDE) of the second kind has been analyzed. The numerical solutions of VIDE will be computed at two points concurrently using the proposed numerical method and executed in the predictor-corrector (PECE) mode. The strategy to obtain the numerical solution of an integral part is discussed and the stability analysis of the diagonally implicit multistep block method was investigated. Numerical results showed the competence of diagonally implicit multistep block method when solving Volterra integrodifferential equations compared to the existing methods.

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A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

Baghdad Science Journal ◽

10.21123/bsj.2020.17.1.0166 ◽

2020 ◽

Vol 17 (1) ◽

pp. 0166

Author(s):

Hussain Et al.

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Ordinary Differential Equations ◽

Numerical Results ◽

New Method ◽

Kutta Method ◽

First Order ◽

Runge Kutta Method ◽

Runge Kutta ◽

The Stability

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

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Numerical Solution of a Linear Third Order Multi-Point Boundary Value Problems Using Fixed Point Iterative Method

Applied Mathematics & Information Sciences ◽

10.18576/amis/120318 ◽

2018 ◽

Vol 12 (3) ◽

pp. 625-631

Author(s):

Nakone Bello ◽

Abubakar Roko ◽

Aminu Mustafa

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Numerical Solution ◽

Boundary Value Problems ◽

Boundary Value ◽

Point Boundary ◽

Third Order ◽

Fixed Point Iterative Method

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Convergence Analysis and Numerical Study of a Fixed-Point Iterative Method for Solving Systems of Nonlinear Equations

The Scientific World JOURNAL ◽

10.1155/2014/789459 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Na Huang ◽

Changfeng Ma

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Convergence Analysis ◽

Nonlinear Equations ◽

Convergence Theorem ◽

Numerical Study ◽

Numerical Results ◽

Systems Of Nonlinear Equations ◽

Fixed Point Iterative Method

We present a fixed-point iterative method for solving systems of nonlinear equations. The convergence theorem of the proposed method is proved under suitable conditions. In addition, some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach.

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A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽

10.2298/fil1715933k ◽

2017 ◽

Vol 31 (15) ◽

pp. 4933-4944

Author(s):

Dongseung Kang ◽

Heejeong Koh

Keyword(s):

Functional Equation ◽

Fixed Point ◽

General Solution ◽

Single Case ◽

Fixed Point Method ◽

Point Method ◽

Fixed Point Approach ◽

The Stability ◽

The Given ◽

Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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