“…Such fractional models are used extensively by many experts to explain their complicated structures easily, simplified the controlling design without any loss of hereditary behaviors as well as create nature issues closely understandable for these phenomena. Accordingly, fractional-order derivatives provide more accurate models of realism problems than integer-order derivatives; they are actually found to be a suitable tool to describe certain physical and engineering problems including advection–diffusion models, dynamical mathematical models, electrical circuits models and networks models (El-Ajou et al , 2015; Abu Arqub et al , 2015; Zhao and Deng, 2015; Ray, 2016; Chen et al , 2016; Yana and Yang, 2015; El-Ajou et al , 2015; Ortigueira and Machado, 2003; Raja et al , 2015; Raja et al , 2017; Ray, 2007; Ray et al , 2008; Ray and Gupta, 2016a, 2016b; Ray, 2013; Ray and Gupta, 2014). Developing analytical and numerical methods for the solutions of time-fractional PDEs is a very important task owing to their practical interest.…”