### Fractional B-spline collection method for solving fractal-differential equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Al-Zintan University, Libya

2 Faculty of Arts and Science Al-Wahat, Benghazi University, Libya

Abstract

This study used the fractional B-spline collocation technique to obtain the numerical solution of fractal-fractional differential equations. The technique was considered to solve the fractal-fractional differential equations (FFDEs)  with ($0 <\gamma_i < 1,\, i = 1, 2, \cdots, N$). In this suggested technique, the B-spline of fractional order was utilised in the collocation technique. The scheme was easily attained, efficient, and relatively precise with reduced computational work numerical findings. Via the proposed technique, FFDEs can be reduced for solving a system of linear algebraic equations using an appropriate numerical approach. The verified numerical illustrative experiments were presented will show the effectiveness of the technique proposed in this study in solving FFDEs in three cases of nonlocal integral and differential operators namely power law kernel, when the kernels are exponential and the generalization of Mittag-Leffler kernel. The approximate solution is very good and accurate to the exact solution.

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