Numerical and analytical investigations for solution of fractional Ito equation describing motions of long waves in shallow water under gravity

• time-fractional Ito equation has been solved utilizing the RBF-FD method. • meshfree method based on MQ-RBF for spatial discretization are considered. • spatial derivatives are discretized via the multiquadric RBF. • some useful theorems are established for stability and convergence. • results are compared with Kudryashov and tanh method solutions. In this manuscript, a meshfree numerical scheme based on radial basis function-finite difference (RBF-FD) method is proposed to solve the time-fractional Ito equation. First, the temporal derivative is approximated through the finite difference technique. Then, the spatial derivatives are discretized via the multiquadric RBF. Furthermore, some useful theorems are discussed to establish the stability and convergence of the proposed numerical scheme. Finally, some test problems are presented and the results are compared with the acquired Kudryashov method and tanh method solutions to establish the computational efficiency and applicability of the proposed method.