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Numerical solution of fractional differential equations via a Volterra integral equation approach

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran

    Shahrokh Esmaeili

  2. Department of Applied Mathematics, Amirkabir University of Technology, No. 424 Hafez Avenue, Tehran, Iran

    Mostafa Shamsi & Mehdi Dehghan

Authors
  1. Shahrokh Esmaeili
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  2. Mostafa Shamsi
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  3. Mehdi Dehghan
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Correspondence to Shahrokh Esmaeili.

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Esmaeili, S., Shamsi, M. & Dehghan, M. Numerical solution of fractional differential equations via a Volterra integral equation approach. centr.eur.j.phys. 11, 1470–1481 (2013). https://doi.org/10.2478/s11534-013-0212-6

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  • DOI: https://doi.org/10.2478/s11534-013-0212-6

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