Numerical Solution of a Nonlinear Fractional Integro-Differential Equation by a Geometric Approach

  • S. Shahmorad
  • S. Pashaei
  • M. S. Hashemi
Original Research


Numerical solution of a Riemann–Liouville fractional integro-differential boundary value problem with a fractional nonlocal integral boundary condition is studied based on a numerical approach which preserve the geometric structure on the Lorentz Lie group. A fictitious time \(\tau \) is used to transform the dependent variable y(t) into a new one \(u(t,\tau ):=(1+\tau )^{\gamma }y(t)\) in an augmented space, where \(0<\gamma \le 1\) is a parameter, such that under a semi-discretization method and use of a Newton-Cotes quadrature rule the original equation is converted to a system of ODEs in the space \((t,\tau )\) and the obtained system is solved by the Group Preserving Scheme (GPS). Some illustrative examples are given to demonstrate the accuracy and implementation of the method.


Fractional integro-differential equation Fictitious time Riemann–Liouville derivative Group-preserving scheme 


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesUniversity of TabrizTabrizIran
  2. 2.Department of Mathematics, Basic Science FacultyUniversity of BonabBonabIran

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