Approximate analytic solutions of multi-dimensional fractional heat-like models with variable coefficients

Abstract

In this work, the fractional power series method is applied to solve the 2-D and 3-D fractional heat-like models with variable coefficients. The fractional derivatives are described in the Liouville-Caputo sense. The analytical approximate solutions and exact solutions for the 2-D and 3-D fractional heat-like models with variable coefficients are obtained. It is shown that the proposed method provides a very effective, convenient and powerful mathematical tool for solving fractional differential equations in mathematical physics.

Approximate analytic solution for multi-dimensional fractional wave-like equation

“…Yang et al [17] suggested the fractional series expansion method for local fractional calculus, and it was extended to general fractional calculus in 2015 by Li and Zhu [18]. The both methods can be extended to fractional differential equations and fractal differential equations [19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”