On Analytical Solution of Time-Fractional Biological Population Model by means of Generalized Integral Transform with Their Uniqueness and Convergence Analysis

This research utilizes the generalized integral transform and the Adomian decomposition method to derive a fascinating explicit pattern for outcomes of the biological population model (BPM). It assists us in comprehending the dynamical technique of demographic variations in BPMs and generates significant projections. Besides that, generalized integral transforms are the unification of other existing transforms. To investigate the closed form solutions, we employed a fractional complex transform to deal with a partial differential equation of fractional order and a generalized decomposition method was applied to analyze the nonlinear equation. Several aspects of the Caputo and Atangana–Baleanu fractional derivative operators are discussed with the aid of a generalized integral transform. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest that it can be used for a variety of nonlinear evolutionary problems.