Geodesic
Generalized Fractional Evolution Equation
Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 375-398

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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.
Keywords: Generalized Functions, Convolution Product, Generalized Gross Laplacian, Riemann-Liouville Derivative, Caputo Derivative, 46F25, 26A33, 46G20 
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     title = {Generalized {Fractional} {Evolution} {Equation}},
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Da Silva, J. L.; Erraoui, M.; Ouerdiane, H. Generalized Fractional Evolution Equation. Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 375-398. http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a2/