Analytical Approximations of Partial Differential Equations of Fractional Order with Multistep Approach

Al‐Smadi, Mohammed; Freihat, Asad; Hammad, Ma’mon Abu; Momani, Shaher; Arqub, Omar Abu

doi:10.1166/jctn.2016.5780

Cited by 43 publications

(22 citation statements)

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“…The convergence of a series is important. As long as the series solution (22) given by the (LHAM) is convergent, it must be the solution of the considered system of fractional differential equations.…”

Section: Mohammed Alabedalhadimentioning

confidence: 99%

“…The homotopy analysis method (HAM) proposed first by Liao [12][13][14][15][16] for solving linear and nonlinear differential and integral equations. This method provides an effective procedure for explicit numerical solutions of a wide and general class of differential systems representing real physical problems [17][18][19][20][21][22][23]. The validity of the HAM is independent of whether there exist small parameters or not in the considered equation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Mohammed Alabedalhadimentioning

confidence: 99%

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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“…Therefore, it is necessary to obtain some mathematical tools to understand the complex structure of uncertainty models [1][2][3][4][5]. On the other hand, the theory of fractional calculus, which is a generalization of classical calculus, deals with the discussion of the integrals and derivatives of noninteger order, has a long history, and dates back to the seventeenth century [6][7][8][9][10]. Different forms of fractional operators are introduced to study FDEs such as Riemann-Liouville, Grunwald-Letnikov, and Caputo.…”

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%

“…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]. 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.…”

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

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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/).

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Analytical Approximations of Partial Differential Equations of Fractional Order with Multistep Approach

Cited by 43 publications

References 0 publications

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

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

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

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

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