# Generalized Fractional Evolution Equation

Da Silva, J. L.; Erraoui, M.; Ouerdiane, H.

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 4, page 375-398
- ISSN: 1311-0454

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topDa Silva, J. L., Erraoui, M., and Ouerdiane, H.. "Generalized Fractional Evolution Equation." Fractional Calculus and Applied Analysis 10.4 (2007): 375-398. <http://eudml.org/doc/11333>.

@article{DaSilva2007,

abstract = {2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In 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.∗ Partially supported by: GRICES, Proco 4.1.5/Maroc; PTDC/MAT/67965/2006; FCT, POCTI-219, FEDER.},

author = {Da Silva, J. L., Erraoui, M., Ouerdiane, H.},

journal = {Fractional Calculus and Applied Analysis},

keywords = {46F25; 26A33; 46G20},

language = {eng},

number = {4},

pages = {375-398},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Generalized Fractional Evolution Equation},

url = {http://eudml.org/doc/11333},

volume = {10},

year = {2007},

}

TY - JOUR

AU - Da Silva, J. L.

AU - Erraoui, M.

AU - Ouerdiane, H.

TI - Generalized Fractional Evolution Equation

JO - Fractional Calculus and Applied Analysis

PY - 2007

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 10

IS - 4

SP - 375

EP - 398

AB - 2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In 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.∗ Partially supported by: GRICES, Proco 4.1.5/Maroc; PTDC/MAT/67965/2006; FCT, POCTI-219, FEDER.

LA - eng

KW - 46F25; 26A33; 46G20

UR - http://eudml.org/doc/11333

ER -

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