## Computational solution of a fractional integro-differential equation.(English)Zbl 1449.65365

Summary: Although differential transform method (DTM) is a highly efficient technique in the approximate analytical solutions of fractional differential equations, applicability of this method to the system of fractional integro-differential equations in higher dimensions has not been studied in detail in the literature. The major goal of this paper is to investigate the applicability of this method to the system of two-dimensional fractional integral equations, in particular to the two-dimensional fractional integro-Volterra equations. We deal with two different types of systems of fractional integral equations having some initial conditions. Computational results indicate that the results obtained by DTM are quite close to the exact solutions, which proves the power of DTM in the solutions of these sorts of systems of fractional integral equations.

### MSC:

 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 45D05 Volterra integral equations 26A33 Fractional derivatives and integrals
Full Text:

### References:

 [1] Podlubny, I., Fractional Differential Equations, (1999), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0918.34010 [2] Kurulay, M.; Bayram, M., Some properties of the Mittag-Leffler functions and their relation with the Wright functions, Advances in Difference Equations, 2012, 181, (2012) · Zbl 1377.33012 [3] Kadem, A.; Kilicman, A., The approximate solution of fractional fredholm integro differential equations by variational iteration and homotopy perturbation methods, Abstract and Applied Analysis, 2012, (2012) · Zbl 1242.65284 [4] Momani, S.; Odibat, Z., A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylor’s formula, Journal of Computational and Applied Mathematics, 220, 1-2, 85-95, (2008) · Zbl 1148.65099 [5] Secer, A.; Akinlar, M. A.; Cevikel, A., Efficient solutions of systems of fractional PDEs by differential transform method, Advances in Difference Equations, 2012, 188, (2012) · Zbl 1377.35279 [6] Kurulay, M.; Bayram, M., Approximate analytical solution for the fractional modified KdV by differential transform method, Communications in Nonlinear Science and Numerical Simulation, 15, 7, 1777-1782, (2010) · Zbl 1222.35172 [7] Kurulay, M.; Ibrahimoǧlu, B. A.; Bayram, M., Solving a system of nonlinear fractional partial differential equations using three dimensional differential transform method, International Journal of Physical Sciences, 5, 6, 906-912, (2010) [8] Bandrowski, B.; Karczewska, A.; Rozmej, P., Numerical solutions to fractional perturbed volterra equations, Abstract and Applied Analysis, 2012, (2012) · Zbl 1259.65210
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.