SOLVING FRACTIONAL PDES OF CAPUTO TYPE BY MIKUSI?SKI’S OPERATIONAL CALCULUS

Abstract

Recently, the algebraic method of Mikusi?ski’s operational calculus was extended for the first time to fractional PDEs on orthant domains. We now investigate how the method can be adapted to solve fractional PDEs involving Caputo derivatives, with more natural boundary conditions than the previous work with Riemann–Liouville derivatives. We create an algebraic framework for interpreting multi-dimensional integro-differential operators and solve some PDEs in two dimensions, with the solutions being written in terms of some newly defined multivariate Mittag-Leffler functions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.