On the solutions for generalised multiorder fractional partial differential equations arising in physics

Abstract

In this article, we have studied solutions of a generalised multiorder fractional partial differential equations involving the Caputo time-fractional derivative and the Riemann–Liouville space fractional derivatives using Laplace–Fourier transform technique. Proposed generalised multiorder fractional partial differential equation is reducible to Schrödinger equation, wave equation and diffusion equation in a more general sense, and hence, solutions of these equations are specifically noted. Not only this, solutions of equation proposed in the stochastic resetting theory in the context of Brownian motion can also be found in a general regime.