dhafar zuhair ali ajina

For introducing of studying the fractal differential Equations, a proposed method for its solution was studied using Power series Methods via least squares approximations. The method depend on the definitions of Riemann-liouville fractional derivatives. The linear non homogenous fractal differential Equations are solved with detailed examples. For checking the errors, many comparisons of solutions with exact solutions and with known solutions.

REVIEW OF SOLUTION FRACTAL DIFFERENTIAL EQUATIONS VIA THE RIEMANN-LIOUVILLE

It was studied in this, the classification, definition, characteristic, basic of linear fractual differential equations of both types (homogeneous and non-homogeneous) of the Riemann-Liouville type, Updated methods for solving fractional differential equations represented as ( special types, Laplace Ttransform, The Power Series, The Generalized Mittag-Leffler, Shehu Transform). In this thesis, was proposed to solve the non-homogeneous linear fractal differential equations of the type Riemann-Liouville is studied. Our method based on the power series method of their solutions based of Mittag-Leffler function and least squares method. In addition, examples were solved to explain the powerful of proposed for testing our method. And a comparison between proposed method and the exact solution is used.