Research Papers

Solving Nonlinear Fractional Integro-Differential Equations of Volterra Type Using Novel Mathematical Matrices

[+] Author and Article Information
Farshid Mirzaee

Department of Mathematics,
Faculty of Science,
Malayer University,
Malayer 65719-95863, Iran
e-mail: f.mirzaee@malayeru.ac.ir

Saeed Bimesl

Department of Mathematics,
Faculty of Science,
Malayer University,
Malayer 65719-95863, Iran
e-mail: saeed.bimesl@stu.malayeru.ac.ir

Emran Tohidi

Young Researchers and Elite Club,
Mashhad Branch,
Islamic Azad University,
Mashhad, Iran
e-mail: emrantohidi@gmail.com

1Corresponding author.

Manuscript received July 26, 2014; final manuscript received November 27, 2014; published online April 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(6), 061016 (Nov 01, 2015) (6 pages) Paper No: CND-14-1174; doi: 10.1115/1.4029281 History: Received July 26, 2014; Revised November 27, 2014; Online April 09, 2015

In this paper, the operational matrix of Euler functions for fractional derivative of order β in the Caputo sense is derived. Via this matrix, we develop an efficient collocation method for solving nonlinear fractional Volterra integro-differential equations. Illustrative examples are given to demonstrate the validity and applicability of the proposed method, and the comparisons are made with the existing results.

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Grahic Jump Location
Fig. 1

The plot of approximate solutions (example 1)

Grahic Jump Location
Fig. 2

The plot of exact and approximate solution for N = 10 (example 3)

Grahic Jump Location
Fig. 3

The plot of error function |e10(x)| (example 3)



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