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

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.

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