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Title: Generalized Fractional Evolution Equation
Authors: Da Silva, J. L.
Erraoui, M.
Ouerdiane, H.
Keywords: Generalized Functions
Convolution Product
Generalized Gross Laplacian
Riemann-Liouville Derivative
Caputo Derivative
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 4, (2007), 375p-398p
Abstract: In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic representation while for the Caputo time fractional evolution equation it is related to the inverse stable subordinators.
Description: 2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20
ISSN: 1311-0454
Appears in Collections:2007

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