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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.

fractional calculus and applied analysis

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