Abstract
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.
Highlights
A framework of nonlinear developmental equations was designed to model the proportion of a demographic in particular domains [1, 2]
Leading up to delving into the step-by-step methodologies for formulating and interpreting continuously biological population model (BPM), we will take a look at population genetic sculpting in the past, granting us an overview of the key figures in the field of ecology and evolution as well as the techniques they formed to comprehend population systems from a physics perspective
We investigate a fundamental model in biology. e degenerate parabolic equation appears in the spatial diffusion of biological populations [17, 18]: Qς Q2w w + Q2w w + σ(Q), ς ≥ 0, w1, w2 ∈ R, (1)
Summary
A framework of nonlinear developmental equations was designed to model the proportion of a demographic in particular domains [1, 2]. [22] recently considered the fractional spatial diffusion of a BPM via a new integral transform in the singular and nonsingular kernel settings. Amidst George Adomian’s massive boost in 1980, the Adomian decomposition method introduced a well-noted terminology. It has been intensively implemented for a diverse set of nonlinear PDEs, for instance, the Korteweg–De Vries model [29], Fisher’s model [30], Zakharov–Kuznetsov equation [31], and so on. Motivated by the above propensity, we aim to establish a semianalytical approach by mingling the generalized integral transform with the Adomian decomposition method. With the assistance of fractional derivative operators, we constructed the approximate analytical solution to BPM. Sketching and comparison analysis solutions are drafted with a powerful and pragmatic approach Both operators consistently behave according to the projected method
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