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Operational calculus for the Riemann–Liouville fractional derivative with respect to a function and its applications

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FD2W01 - Deterministic and stochastic fractional differential equations and jump processes

Mikusiński’s operational calculus is a formalism for understanding integral and derivative operators and solving differential equations, which has been applied to several types of fractional-calculus operators by Y. Luchko and collaborators. In this talk, we consider the operators of Riemann–Liouville fractional differentiation of a function with respect to another function, and discover that the approach of Luchko can be followed, with small modifications, in this more general setting too. The Mikusiński’s operational calculus approach is used to obtain exact solutions of fractional differential equations with constant coefficients and with this type of fractional derivatives. These solutions can be expressed in terms of Mittag-Leffler type functions. Joint work with: Arran Fernandez (Eastern Mediterranean University, Northern Cyprus, Turkey)

This talk is part of the Isaac Newton Institute Seminar Series series.

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