A new approximation of conformable time fractional partial differential equations with proportional delay

Abstract

In this work, we introduced novel approximate numerical approach, so called “extended reduced conformable differential transform method (ERC-DTM)” which is the implementation of DTM for conformable time fractional partial differential equations with proportional delay. Also, we have investigated some properties of ERC-DTM. In addition, the conformable time fractional generalized Burgers equation with proportional delay is approximated by adopting ERC-DTM. The preciseness, effectiveness and validity of the proposed ERC-DTM is tested over three different examples of conformable time fractional PDEs with proportional delay by computing various error norms: L2, L∞, and absolute error. The computed results show that the introduced ERC-DTM produces the series solutions converging to the exact solutions very rapidly for different values of fractional order, and these findings are also verified graphically. The main strength of the proposed ERC-DTM is that it requires no linearization or small perturbations, and less amount of computational cost is required as compared to existing techniques. The proposed ERC-DTM is an reliable and efficient mathematical tool to compute approximate behavior of nonlinear conformable time fractional model of partial differential equations with proportional delay.