Solving fractional partial differential equations via a new scheme

[摘要] In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms of the Caputo derivative. We illustrate the method with a simple algorithm that can be used to solve different types of time-fractional partial problems. We introduce a new theorem to explain the required substitutions of the proposed method. In addition, convergence analysis conditions of the method are given. Furthermore, some different illustrative examples of time-fractional partial differential equations and systems are discussed to show the applicability and simplicity of the new approach.

[学科分类] 地球科学(综合)

[关键词] fractional differential equations;time fractional partial differential equations;analytical solution;power series