(untitled) (JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences, 2025)
Background: Fractional calculus is an area of ​​mathematics that discusses the research and applications of non-integer calculus in ℝ or ????. I present the variable iterative method for calculating numerical approximations to solve classical differential equations that was developed to solve linear fractional differential equations. Materials and Methods: Were studied using the variable iterative method, where fractional derivatives according to Caputo’s derivative were used. Some examples were studied to test the accuracy of the results we obtained. This comparison was presented using the curves for these examples used to compare the absolute error of the approximate solution and the exact solution. Results: The results of Table (3) prove that there is acceptable agreement between the approximate and exact solution for Example (2). when n is larger, the closer the approximate solution approaching. Through the results of the three example tables, the effectiveness of numerical methods in obtain acceptable results demonstrated. Conclusion: When studying the examples given in the research, when using the variable iterative method and through examples and tables. I noticed the effectiveness of the variable iterative method when used, especially in the second example in the case α = 0.9