Applications of Numerical Integrations on the Trapezoidal and Simpson's Methods to Analytical and MATLAB Solutions

Applied mathematics has become widely used among the computer engineering community and various sciences. Not only that, but accuracy and speed are now required. Numerical methods have been submitted to demonstrate the efficiency and accuracy of these methods by assigning them to a computer that previously been corrected in computer formats. This key feature makes the solution perfect and easy to used Simpson 1/3 and Simpson 3/8 are applied to the proposed equation. A trapezoidal method of fractional differential equations, solved using different numerical methods to demonstrate the accuracy of properties, was used. We dealt with many numerical algorithms. Below are decisions with written and unwritten differential equations. Generate error analysis and stability analysis for a high-resolution digital system. Research objectives: Turns out numerical solutions are very accurate near the exact solution. This paper aims to provide numerical calculations for different methods. The graph is compared with the computer literary graphs for clarity. Effectiveness of numerical algorithms used with exact solutions and profitable MATLAB solutions.