An Efficient Numerical Method for Nonlinear Time Fractional Hyperbolic Partial Differential Equations Based on Fractional Shehu Transform Iterative Method

In science and engineering, nonlinear time-fractional partial differential equations (NTFPDEs) are thought to be a useful tool for describing several natural and physical processes. It is tough to come up with analytical answers for these issues. Finding answers to NTFPDEs is therefore a crucial component of scientific study. To solve nonlinear time-fractional hyperbolic partial differential equations (NTFHPDEs), we provide a novel fractional Shehu transform iterative method (FSTIM) in this work. In this case, the Caputo derivative is used to get the fractional derivative. The method combines two powerful numerical approaches called the fractional Shehu transform and the new iterative method (NIM), also known as the Daftardar-Gejji and Jafari method. Through the recommended scheme, the linear portion of the problem is resolved by employing the Shehu transform method, while the noise terms from the nonlinear portion of the problem disappear over a successive iteration process of the NIM. The solution of FSTIM is then denoted in a series form, which is convergent to the precise answer of the assumed problem. Using principles from Banach's spaces, the stability and convergence analysis of the suggested approach are addressed. To confirm the effectiveness and accuracy of the method, three illustrations from NTFHPDEs are presented. The obtained results are compared with the exact solutions and the other numerical results existing in the literature in terms of L infinity and L2 absolute errors. The findings showed that the proposed method outperforms the other numerical techniques in the literature and gives accurate results with a few terms. Therefore, the recommended approach is effective and straightforward and can be applied to other complex nonlinear physical differential equations with fractional order.