DISCRETE WEIGHTED RESIDUAL METHODS WHICH ARE TECHNIQUES USED FOR NUMERICAL SOLUTION TO MIXED VOLTERRA-FREDHOLM FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

This study aims to solve the most general form of linear mixed Volterra-Fredholm integro-differential equations multi-fractional order in Caputo sense (MV-FIFDEs), which is solved by using orthogonal generalized Bernstein’s polynomial expansion with collocation and moment discrete weighted residual method under suitable conditions; then, Clenshaw-Curtis formula applied approximate integral terms equation numerically. In this work, integro-fractional differential are reduced algebraic then an operational matrix, solution resultant system yields unknown Bernstein coefficients approximation solutions. An algorithm has been created for each technique handle MV-FIFDEs described methods. Furthermore, numerical examples presented demonstrate compare techniques’ validity applicability comparisons previous results. The majority programs performed on a computer MATLAB v. 9.7. Keywords: Mixed Fractional Integro-Differential Equations, Derivative, Polynomial, Collocation, Moment, Discrete Weighted Residual, Formula, Equations DOI： https://doi.org/10.35741/issn.0258-2724.58.3.43