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چکیده
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In this study, an innovative strategy integrating the moving least squares (MLS) method with the Genocchi-collocation technique is advanced to approximate the solution of fractal-fractional integro-differential equations. An essential advantage of the proposed technique is that it does not apply meshing and does not depend on the geometry of the computational domain, hence, this method can be considered as a meshless method. Also, accurate results can be achieved with a small number of points and basis functions, thereby significantly reducing computational complexity. By employing the MLS method, Genocchi polynomials, the Gauss-Legendre quadrature rule, and the collocation method, the problem under investigation is transformed into a system of algebraic equations. The convergence analysis of the obtained approximation is established by proving theorems. Several illustrative examples are provided to demonstrate the applicability and efficacy of the proposed strategy.
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