Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative

Iranian Journal of Numerical Analysis and Optimization

مقاله 8، دوره 14، Issue 4 - شماره پیاپی 31، اسفند 2024، صفحه 1203-1223   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87189.1405

نویسندگان

E. Sedighi؛ O. Baghani^* ؛ H. Azin

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Iran.

چکیده

The present article introduces an operational approach based on modified hat functions to solve the space-time-fractional differential equations in the Caputo sense. In this method, the derivative of the unknown function is considered as a linear combination of modified hat functions. We use the operational matrix of the Riemann–Liouville fractional integral of modified hat functions to approximate the Caputo fractional derivative in order to reduce the problem to a system of Sylvester equations. The error of the mentioned method is of the order O(h3). In addition, we examine several  numerical examples to confirm the ability of the proposed approach. 

کلیدواژه‌ها

Modified hat functions؛ Space-time-fractional differential equations؛ Operational matrix؛ Caputo fractional derivative

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