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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 17 مرداد 1403   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87189.1405

نویسندگان

E. Sedighi؛ Omid Baghani^* ؛ Hadis 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 the modified hat functions. We use Caputo's fractional derivative and Riemann-Liouville integral to approximate the functions in the equation in order to reduce the problem to simple linear equations. Also, we use the operational matrix of the fractional integral for The integral approximation of hat functions is used. The error of the mentioned method is of the order of $O(h^3)$. 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