Abstract
The concept of double-order fractional derivative generalizing the well-known Hilfer’s derivative is introduced. The formula is given for the Laplace transform of double-order fractional derivative, which is used to solve the Cauchy-type problem for equations of fractional order with this derivative. The closed solutions to some boundary-value problems for the equation of anomalous diffusion with double-order fractional derivative in time are obtained.
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2014, pp. 100–107.
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Bulavatsky, V.M. Closed form of the Solutions of some Boundary-Value Problems for Anomalous Diffusion Equation with Hilfer’s Generalized Derivative. Cybern Syst Anal 50, 570–577 (2014). https://doi.org/10.1007/s10559-014-9645-1
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DOI: https://doi.org/10.1007/s10559-014-9645-1