Efficient New Approximations for Space-Time Fractional Multi-dimensional Telegraph Equation

In the present article two new hybrid efficient techniques: namely optimal homotopy analysis J-transform method (OHAJTM) and variational iteration J-transform method (VIJTM) are proposed for solving multi-dimensional space-time fractional telegraph equation, appearing in modelling of numerous real-world phenomena like-electrical signal-propagation, random walk, propagation of waves and so forth. The OHAJTM is developed via utilizing properties of newly developed J-transform to optimal homotopy analysis method while VIJTM is based upon the concept of variation iteration theory and the properties of the J-transform, in addition, some properties of J-transform for Caputo derivatives are also investigated. Banach fixed point theory is utilized to analyze the stability of VIJTM. Both methods: OHAJTM and VIJTM produces stable solutions converging to the exact solutions, which is illustrated by considering five different test examples of multi-dimensional space-time fractional telegraph equation. In addition, the computed approximate results are expressed in the compact form of Mittag-Leffler function. The numerical findings demonstrate that the developed techniques perform better for multi-dimensional space-time fractional telegraph equation, and at a fixed iteration: OHAJTM produces better accuracy as compared to VIJTM and recently developed techniques. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.