Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach

Moaddy, K.; Freihat, Asad; Al‐Smadi, Mohammed; Abuteen, Eman; Hashim, Ishak

doi:10.1007/s00500-016-2378-5

Cited by 44 publications

(28 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…multistep reduced differential transform method [19,20], reproducing kernel Hilbert space method [21,22] and multistep generalized differential transform method [23] are also capable to handle a wide range of problems. The multistep reduced differential transform method is proposed by Al-Smadi et al [19,20].…”

Section: Introductionmentioning

confidence: 99%

“…AlSmadi et al [21] applied reproducing kernel Hilbert space method to approximate the solution two-point boundary value problems for fourth-order Fredholm-Volterra integrodifferential equations whereas the authors of [22] applied aforesaid method to obtain the solution for systems of second-order differential equations with periodic boundary conditions. Moaddy et al [23] presented a multistep generalized differential transform method to obtain the approximate solution of Rabinovich-Fabrikant model involving Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A computational modelling of micro strip patch antenna and its solution by RDTM

Chaurasia

Mathur

Pareekh

et al. 2018

Alexandria Engineering Journal

View full text Add to dashboard Cite

This paper concerns with the modelling of a micro strip antenna with strip line feeding technique formulated using Ohm's law. A partial differential equation is obtained from the model which is solved using ''Reduced Differential Transformation Method (RDTM)". A couple of numerical examples are considered to check the accuracy, efficiency and convergence of the method. The present method is a very powerful mathematical tool for solving wide range of problems arising in circuit theory, RF field, and science and communication system fields. Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A computational modelling of micro strip patch antenna and its solution by RDTM

Chaurasia

Mathur

Pareekh

et al. 2018

Alexandria Engineering Journal

View full text Add to dashboard Cite

show abstract

“…Different forms of fractional operators are introduced to study FDEs such as Riemann-Liouville, Grunwald-Letnikov, and Caputo. Out of these forms, the Caputo concept is an appropriate tool for modeling practical situations due to its countless benefits as it allows the process to be performed based on initial and boundary conditions as is traditional and its derivative is zero for constant [11][12][13][14][15][16][17].…”

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach

Cited by 44 publications

References 25 publications

A computational modelling of micro strip patch antenna and its solution by RDTM

A computational modelling of micro strip patch antenna and its solution by RDTM

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

Contact Info

Product

Resources

About