Group classification of nonlinear time-fractional diffusion equation with a source term

S.Yu. Lukashchuk and A.V. Makunin

Applied Mathematics and Computation, 2015, vol. 257, issue C, 335-343

Abstract: A complete group classification is presented for a nonlinear time-fractional diffusion equation with a source term. The equation involves the Riemann–Liouville time-fractional derivative of the order α∈(0,2). All coefficients of the equation are sought as a function of the dependent variable. Using the infinitesimal approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration, and group classification is carried out up to the equivalence transformations. Examples of invariant solutions are also presented.

Keywords: Time-fractional diffusion equation; Symmetry; Equivalence transformation; Group classification; Invariant solution (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:335-343

DOI: 10.1016/j.amc.2014.11.087

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