In this paper, we apply (G'/G) -expansion methods for solving the interested nonlinear Fredholm-Volterra integro-differential equation.

In this paper, the fuzzy approximate solutions for the fuzzy Hybrid differential equation emphasizing the type of generalized Hukuhara differentiability of the solutions are obtained by using the two-dimensional Müntz–Legendre wavelet method. To do this, the fuzzy Hybrid differential equation is transformed into a system of linear algebraic equations in a matrix form. Thus, by solving this system, the unknown coefficients are obtained. The convergence of the proposed method is established in detail. Numerical results reveal that the two-dimensional Müntz–Legendre wavelet is very effective and convenient for solving the fuzzy Hybrid differential equation.

This research introduces a new definition of fuzzy fractional derivative, fuzzy conformable fractional derivative, which is defined based on generalized Hukuhara differentiability. Namely, we investigate the Hybrid fuzzy fractional differential equation with the fuzzy conformable fractional generalized Hukuhara derivative. We establish that the Hybrid fuzzy fractional differential equation admits two fuzzy triangular solutions and prove that these fuzzy solutions are obtained together with a characterization of these solutions by two systems of fractional differential equations. We propose an adaptable numerical scheme for the approximation of the fuzzy triangular solutions. Numerical results reveal that the numerical method is convenient for solving the Hybrid fuzzy conformable fractional differential equation.