Multi-time fractional diffusion equation
Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences, Nalchik, Russian Federation
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Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
We construct a fundamental solution of a multi-time diffusion equation with the Dzhrbashyan-Nersesyan fractional differentiation operator with respect to the time variables. We give a representation for a solution of the Cauchy problem and prove the uniqueness theorem in the class of functions of fast growth. The corresponding results for equations with Riemann-Liouville and Caputo derivatives are obtained as particular cases of the proved assertions.
© EDP Sciences, Springer-Verlag, 2013