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.

对于与空间异质性或异常扩散有关的场景，非整数阶系统中的图案形成过程正日益成为许多科学家和工程师考虑的活动主题。遇到的主要缺点是Caputo和Fabrizio分数运算符的计算，这会导致及时出现非局部性问题或内存问题。我们基于新颖的有限差分方法制定了有效的数值方案，并开发了用于求解时间分数阶反应扩散方程的频谱算法。通过求解一维，二维或三维空间中的分数BVAM模型来展示所提出的技术，以分数微分的概念探索图案形成的动态丰富性。获得的实验结果模拟了多种假拟铂y鱼structures鱼结构，其中包括老虎假拟斑y虎中的苏柔比姆，伪拟铂斑y中有斑点的苏鲁宾，网状拟铂斑质中的禁止的苏鲁宾，假拟斑y的点状和垂直条状结构，点状拟点藻类物种，还有许多其他未分类的类鳞状物种。针对分数功率的不同值给出了实验结果，以解决可能出现的任何问题或查询。许多其他无法识别的模式被归类为筋膜假单胞菌。针对分数功率的不同值给出了实验结果，以解决可能出现的任何问题或查询。许多其他无法识别的模式被归类为筋膜假单胞菌。针对分数功率的不同值给出了实验结果，以解决可能出现的任何问题或查询。