Applying the Least Squares Approach to Solve Fredholm Fuzzy Fractional Integro-Differential Equations

This study introduces a methodology that integrates solution and analysis for linear and nonlinear fuzzy integro differential equations (FIDEs). A novel form approximates analytical method is presented to obtain a converge solution for fuzzy fractional Fredholm integral differential equations (FFIDEs). A control points method based on the principles least squares method (LSM) is presented. These control points have important role to ensuring the convergence of the approximate series solution. A new form of LSM is changed to FLSM includes an extra feature known as the convergence control points parameters, regarded as one of its most powerful tools that constructed from the use of some concepts of fuzzy set theory and fractional calculus. The properties of Caputo’s fractional derivative in the fuzzy domain, along with convergence analysis, improve and refine the methodology. The results validation of FLSM is demonstrated by addressing two numerical problems as test examples that include FFIDE subject to initial conditions. The results that displayed in the form of tables and figures illustrated the effectiveness and simplicity of the proposed computation method.