Axioms (Sep 2024)

Multidimensional Fractional Calculus: Theory and Applications

  • Marko Kostić

DOI
https://doi.org/10.3390/axioms13090623
Journal volume & issue
Vol. 13, no. 9
p. 623

Abstract

Read online

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann–Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications.

Keywords