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Research Papers

Numerical Solution of High-Order Fractional Volterra Integro-Differential Equations by Variational Homotopy Perturbation Iteration Method

[+] Author and Article Information
A. Neamaty

Department of Mathematics,
University of Mazandaran,
P.O. Box 47416-95447,
Pasdaran Street,
Babolsar 47416-95447, Iran
e-mail: namaty@umz.ac.ir

B. Agheli

Department of Mathematics,
University of Mazandaran,
P.O. Box 47416-95447,
Pasdaran Street,
Babolsar 47416-95447, Iran
e-mail: b.agheli@stu.umz.ac.ir

R. Darzi

Department of Mathematics,
Neka Branch,
Islamic Azad University,
P.O. Box 48411-86114,
Neka 48411-86114, Iran
e-mail: r.darzi@iauneka.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 28, 2014; final manuscript received January 26, 2015; published online June 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(6), 061023 (Nov 01, 2015) (5 pages) Paper No: CND-14-1264; doi: 10.1115/1.4030062 History: Received October 28, 2014; Revised January 26, 2015; Online June 09, 2015

In this paper, variational homotopy perturbation iteration method (VHPIM) has been applied along with Caputo derivative to solve high-order fractional Volterra integro-differential equations (FVIDEs). The “VHPIM” is present in all two steps. In order to indicate the efficiency and simplicity of the proposed method, we have presented some examples. All of the numerical computations in this study have been done on a personal computer applying some programs written in Maple18.

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Figures

Grahic Jump Location
Fig. 1

Comparison of the fourth-order approximate solution (7) with exact solution for different value of α

Grahic Jump Location
Fig. 2

Comparison of the fourth-order approximate solution (9) with exact solution for different value of α

Grahic Jump Location
Fig. 3

Comparison of the fourth-order approximate solution (11) with exact solution for different value of α

Grahic Jump Location
Fig. 4

Comparison of the fourth-order approximate solution (13) with exact solution for different value of α

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