Numerical Simulation of Coupled Fractional Differential-Integral Equations Utilizing the Second Kind Chebyshev Wavelets

In order to solve coupled fractional differential-integral equations more effectively and to deal with the problem that the huge algebraic equations lead to considerable computational complexity and large data storage requirements in the calculation process, this paper approximates the function of the unknown solution based on the Chebyshev wavelet of the second kind and then combines the collocation method to solve the numerical solution of nonlinear fractional Fredholm integral-differential equations. By using the proposed method, the original problem can be reduced to a system of linear algebraic equations, which can be easily solved by some mathematical techniques. In addition, the convergence analysis of the system based on the second kind of Chebyshev wavelet is studied. Several numerical test problems are presented, and the absolute error values under different fractional orders are given, which proves the superiority and effectiveness of the proposed method. It provides support for improving the precision and reliability of the system.