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Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
On Mittag-Leffler-type functions in fractional evolution processes. (English)
[J] J. Comput. Appl. Math. 118, No.1-2, 283-299 (2000). ISSN 0377-0427

The authors review a variety of fractional evolution processes, a phenomenon governed by an integro-differential equation containing integrals and/or derivatives of fractional order in time whose solutions turn out to be related to Mittag-Leffter-type functions. The equations chosen are the simplest of the fractional calculus and include the Abel integral equations of the second kind, which are relevant in typical inverse problems, and the fractional differential equations, which govern generalized relaxation and oscillation phenomena.
[Ismail Taqi Ali (Safat)]

MSC 2000:: *45J05 Integro-ordinary differential equations
26A33 Fractional derivatives and integrals (real functions)
33E20 Functions defined by series and integrals

Keywords: fractional evolution processes; integro-differential equation; Mittag-Leffter-type functions; Abel integral equations; inverse problems; fractional differential equations

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