2D scale-3 fractional Euler wavelets optimization algorithm for fractional-order differential equations

A numerical scheme combining particle swarm optimization(PSO) optimization algorithm for solving fractional-order differential equations is developed by using 2D scale-3 fractional Euler wavelets, which are constructed via orthogonal Euler polynomials. The fractional integration formulas for scale-3 fractional Euler wavelets are derived under Riemann–Liouville fractional integral. The error estimation is given through the generalized fractional-order Taylor expansion and the convergence analysis of 2D scale-3 fractional Euler wavelets expansion is studied. According to the fractional integration formulas, together with the collocation method, a numerical technique is created by discretizing the fractional-order differential equation into a system of equations. Some linear and nonlinear problems are provided and PSO algorithm is applied to the numerical scheme. The numerical results are analyzed and compared with existing findings. This not only confirms the feasibility and effectuality of the proposed method but also demonstrates that PSO algorithm can enhance the numerical scheme’s performance.