Approximate analytic solution of fractional heat-like and wave-like equations with variable coefficients using the differential transforms method


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Secer A.

ADVANCES IN DIFFERENCE EQUATIONS, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2012
  • Doi Number: 10.1186/1687-1847-2012-198
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: wave-like equations, heat-like equations, differential transform method, fractional calculus, VARIATIONAL ITERATION METHOD, DIFFUSION

Abstract

This paper uses the differential transform method (DTM) to obtain analytical solutions of fractional heat- and wave-like equations with variable coefficients. The time fractional heat-like and wave-like equations with variable coefficients were obtained by replacing a first-order and a second-order time derivative by a fractional derivative of order 0 < alpha < 2. The approach mainly rests on the DTM which is one of the approximate methods. The method can easily be applied to many problems and is capable of reducing the size of computational work. Some examples are presented to show the efficiency and simplicity of the method.