Faraidun K. Hamasalh1, Pshtiwan O. Muhammad1

1Faculty of Science and Science Education, School of Science, Sulaimani Univ., Sulaimani, Iraq

**Abstract**

In this paper, we consider a new suitable lacunary fractional interpolation with the idea

of the spline function of polynomial form, and the method applied to solve linear

fractional differential equations. The results obtained are in good agreement with the

exact analytical solutions and the numerical results presented by two examples, results

also show that the technique introduced here is robust and easy to apply.

**Key Words:**Fractional integral and derivative, Caputo Derivative, Taylor’s expansion, Error bound, Spline functions.

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