Abstract
<abstract> <p>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.</p> </abstract>
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