On Mittag-Leffler-type functions in fractional evolution processes. (English) Zbl 0970.45005

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.


45J05 Integro-ordinary differential equations
26A33 Fractional derivatives and integrals
33E20 Other functions defined by series and integrals
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