An Efficient Analytical Method for Solving Singular Initial Value Problems of Nonlinear Systems

Komashynska, Iryna; Al‐Smadi, Mohammed; Arqub, Omar Abu; Momani, Shaher

doi:10.18576/amis/100224

Cited by 51 publications

(32 citation statements)

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“…The residual power series (RPS) method developed in [18] is considered as an effective optimization technique to determine and define the power series solution's values of coefficients of first-and second-order fuzzy differential equations [19][20][21][22]. Furthermore, the RPS is characterized as an applicable and easy technique to create power series solutions for strongly linear and nonlinear equations without being linearized, discretized, or exposed to perturbation [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Alaroud

Al‐Smadi

Ahmad

et al. 2018

International Journal of Differential Equations

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This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order 1 < ≤ 2 under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem's nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution.

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Section: Introductionmentioning

confidence: 99%

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Alaroud

Al‐Smadi

Ahmad

et al. 2018

International Journal of Differential Equations

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“…The objective of the present paper is to use the HAM and Laplace transform to provide optimal solutions for a fractional order differential system model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4 + T-cells. However, other category of methods to handle large amount of fractional problem can be found in [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Simulation as an alternative to linear programming of human T-cell lymphotropic virus I (HTLV-I) model infection of CD4+ T-cells

Alabedalhadi¹

2018

imf

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Simulation is a tradition of operating a process or system in the real world. The act of simulating something first requires the development of a model; this model represents the main characteristics of the selected behaviors, processes, and functions. The model represents the system itself, while the simulation represents the operation of the system over time. In this paper, the optimal solutions of fractional human T-cell lymphotropic virus model infection of CD4+ T-cells will selected by using an efficient technique, called the LHAM, which is a series solution method based on the HAM and Laplace transform in obtaining the solutions for a wide class of problem. The Pade approximation technique to enlarge region of convergence for the solutions. Results obtained using the shame presented here are in good agreement with the numerical results obtained before. Our work confirms the efficiency of LHAM as a tool for solving linear and nonlinear fractional differential equations. The numerical method proposed in this thesis can be utilized to solve other problems in field of nonlinear fractional differential equations.

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“…For examples of these methods, we refer to the work in (Hesameddini and Fotros, 2012;Moaddy et al, 2011;Abdulaziz et al, 2008;Hashim et al, 2009;Odibat and Momani, 2006;Khalil et al, 2015a;2015b;2015c;El-Ajou et al, 2015;Abu-Gdairi et al, 2015;Freihat and Al-Smadi, 2013;Momani et al, 2014;Al-Smadi et al, 2013;. On the other hand, many applications for different problems by using other numerical algorithms can be found in (Abu Arqub et al, 2012;Abu Arqub and Al-Smadi, 2014;Moaddy et al, 2015;Komashynska and Al-Smadi, 2014;Komashynska et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

Abuteen¹,

Freihat²,

Al‐Smadi³

et al. 2016

Journal of Mathematics and Statistics

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This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different values of fractional-order ߙ is shown graphically. A comparative study is presented between the FRDTM and Implicit Runge-Kutta approach to illustrate the efficiency and reliability of the proposed technique. Our numerical investigations indicate that the FRDTM is simple, powerful mathematical tool and fully compatible with the complexity of such problems.

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An Efficient Analytical Method for Solving Singular Initial Value Problems of Nonlinear Systems

Cited by 51 publications

References 0 publications

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Simulation as an alternative to linear programming of human T-cell lymphotropic virus I (HTLV-I) model infection of CD4+ T-cells

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

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