Computational analysis of different Pseudoplatystoma species patterns the Caputo-Fabrizio derivative

Abstract

Abstract Pattern formation processes in non-integer order systems are increasingly becoming the subject of activity considered by many scientists and engineers for scenarios associated with spatial heterogeneity or anomalous diffusion. The major drawback encountered is the computation of the Caputo and Fabrizio fractional operator which leads to non-locality issues or memory problems in time. We formulate efficient numerical schemes which are based on the novel finite difference method and the spectral algorithms are developed for solving time-fractional reaction-diffusion equations. The proposed technique is showcased by solving the fractional BVAM model in one-, two- or three-dimensional spaces, to explore the dynamic richness of pattern formation with the concept of fractional derivatives. Experimental results obtained mimicked various Pseudoplatystoma catfish structures involving the tiger sorubim in Pseudoplatystoma tigrinum, spotted sorubim in Pseudoplatystoma corruscans, the barred sorubim in Pseudoplatystoma reticulatum, spotted and vertical bar structures in Pseudoplatystoma punctifer species, many other unrecognized patterns are classified as Pseudoplatystoma fasciatum species. Experimental results are given for different values of fractional power to address any points or queries that may occur.