...Xiankang Luo; Muhammad Nadeem Purpose This study aims to investigate the approximate solution of the time fractional time-fractional Newell–Whitehead–Segel (TFNWS) model that reflects the appearance of the stripe patterns in two-dimensional systems. The significant results of plot distribution...

...Muhammad Nadeem Purpose The purpose of this paper is to introduce an innovative strategy for the approximate solution of the heat flow problems in two- and three-dimensional spaces. This new strategy is very easy to implement and handles the restrictive variable that may ruin the physical nature...

...Muhammad Nadeem; Zitian Li Purpose This study aims to purpose the idea of a new hybrid approach to examine the approximate solution of the fourth-order partial differential equations (PDEs) with time fractional derivative that governs the behaviour of a vibrating beam. The authors have also...

...Muhammad Nadeem; Ji-Huan He Purpose The purpose of this paper is to find an approximate solution of a fractional differential equation. The fractional Newell–Whitehead–Segel equation (FNWSE) is used to elucidate the solution process, which is one of the nonlinear amplitude equation...

.../implications This paper invokes these two main inspirations: first, Mohand transform is associated with HPM, secondly, fractional view of NWSE with different positive integers. Practical implications In this paper, the graph of approximate solution has the excellent promise with the graphs of exact...

... Licensed re-use rights only Variational iteration method Approximate solution Boundary problem Homotopy perturbation method Variational principle Two-scale method Boundary value problems arise everywhere in engineering (Khan, 2018 ; Bilige and Han, 2018 ; Yadav et al., 2019...

... Licensed re-use rights only Approximate solution Bubbfil algorithm Ancient Chinese mathematics Porous catalyst Taylor series Porous flows (Bovand et al., 2015 ; Chinyoka and Makinde, 2015 ; Celik and Mobedi, 2015 ; Khan and Shafie, 2015) are arising in various fields...

... to the equation, followed by a correction to that solution. An approximate analytic solution, which contains an auxiliary parameter, is obtained. A highly accurate approximate solution of Blasius equation is also provided by adding a third initial condition y ''(0) which demonstrates to be quite accurate...

... method with He's polynomials. Findings – The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational...