A modified numerical algorithm based on fractional Euler functions for solving time-fractional partial differential equations

ABSTRACT A novel and efficient method based on the fractional Euler function together with the collocation method is proposed to solve time-fractional partial differential equations. By applying the Riemann-Liouville fractional integral operator on this problem, we convert it to fractional partial integro-differential equations. Also, we present the method of calculating the operational matrix in a new way. These matrices with the help of the collocation method reduce the problem to a system of algebraic equations that can be easily solved by any usual numerical methods. Furthermore, we discuss error analysis for this method. Finally, the numerical technique is implemented for several examples to illustrate the superiority and efficiency of the proposed method in comparison with some other methods.

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