Solving systems of fractional differential equations using differential transform method

By V. S. Erturk, Shaher Momani. 2008

236 citations recorded by the source corpus.

This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8a44cc643daf01cc34253502ac2330327cc84673

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A Legendre collocation method for fractional integro-differential equations (2011, background): “We refer the reader to Erturk and Momani (2008) and Nazari and Shahmorad (2010) for more research works on the fractional differential and integral equations.”
Solution of Conformable Fractional Ordinary Differential Equations via Differential Transform Method (2016, methodology): “Studies were conducted about solutions of systems of fractional differential equations [22], systems of fractional partial differential equations [23], fractional-order integro-differential equations [24] and fractional differential-algebraic equations [25] using fractional differential transform me”
Positive solutions of fractional differential equations with derivative terms (2012, unknown): “…the time when Leibnitz and Newton invented differential calculus and the tools of fractional calculus have been available and applicable to various fields of study, the qualitative and quantitative investigation of the theory of fractional differential equations has been started recently [1, 2, 3].”
Solution of Conformable Fractional Ordinary Differential Equations via Differential Transform Method (2016, unknown): “Studies were conducted about solutions of systems of fractional differential equations [22], systems of fractional partial differential equations [23], fractional-order integro-differential equations [24] and fractional differential-algebraic equations [25] using fractional differential transform me”