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On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lévy-type processes

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Abstract

It is with great pleasure that we dedicate this paper to Professor Rudolf Gorenflo. In particular, the second named author wants to express his appreciation to an outstanding mathematician who was to him more than 30 years ago an inspiring teacher, and a very humane senior colleague later on.

A class of fractional differential equations are investigated. Using estimates for Mittag-Leffler function and a fixed point theorem, we establish the existence and uniqueness of mild solutions of the equations.

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Correspondence to Niels Jacob.

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Hu, K., Jacob, N. & Yuan, C. On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lévy-type processes. fcaa 15, 128–140 (2012). https://doi.org/10.2478/s13540-012-0009-0

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