The reaction dimerization: A resourceful slant applied on the fractional partial differential equation

Abstract

The paper presents an analysis to investigate the time-fractional coupled diffusion equation with non-linear reaction subject to piecewise initial conditions. The governance system is determined analytically, and numerically adopting an artificial neural network taking the Caputo fractional derivative. In this scheme, the differential equations are transformed into an optimization problem, and minimize the problem by using sophisticated computer simulation Nelder-Mead algorithm. Finally, an experiment has been executed in the application of o-phenylenedioxy-dimethylsilane reaction dimerization which is a trial solution of resources as coefficients. The obtained solution is analyzed by tabulation of numerical values and plotting time based graphs. The novelty of the solution will be provided by comparison with the previous work in the literature as a special case. The numerical outcomes demonstrate the momentous features, efficiency and reliability of the approach.