Novel Computations of the Time-Fractional Fisher’s Model via Generalized Fractional Integral Operators by Means of the Elzaki Transform

Abstract

The present investigation dealing with a hybrid technique coupled with a new iterative transform method, namely the iterative Elzaki transform method (IETM), is employed to solve the nonlinear fractional Fisher’s model. Fisher’s equation is a precise mathematical result that arose in population dynamics and genetics, specifically in chemistry. The Caputo and Antagana-Baleanu fractional derivatives in the Caputo sense are used to test the intricacies of this mechanism numerically. In order to examine the approximate findings of fractional-order Fisher’s type equations, the IETM solutions are obtained in series representation. Moreover, the stability of the approach was demonstrated using fixed point theory. Several illustrative cases are described that strongly agree with the precise solutions. Moreover, tables and graphs are included in order to conceptualize the influence of the fractional order and on the previous findings. The projected technique illustrates that only a few terms are sufficient for finding an approximate outcome, which is computationally appealing and accurate to analyze. Additionally, the offered procedure is highly robust, explicit, and viable for nonlinear fractional PDEs, but it could be generalized to other complex physical phenomena.

Towards new general double integral transform and its applications to differential equations

“…subject to the conditions u(x, 0) = 𝑓 (x), u(0, t) = g(t), (16) where 𝛼, 𝛽, 𝛾 are constant coefficients and h(x, t), f (x), g(t) are continuous functions. By applying general double transform on the both sides of Equation ( 15) and using linearity property of general double transform, we get…”

“…such that 𝛼𝜑(s) + 𝛽𝜓(r) + 𝛾 ≠ 0. Similarly, taking general transform to the initial conditions (16), we obtain respectively…”

“…Many scientist and researcher have made a great effort to develop these methods, and they apply them to solve large modern problems in mathematics. For instance, we have the Fourier transform methods and Laplace transform methods (for more details, the following references have dealt the subject [9][10][11][12][13][14][15][16] ).…”

Analytic Fuzzy Formulation of a Time-Fractional Fornberg–Whitham Model with Power and Mittag–Leffler Kernels

“…The ADM is a semi-analytical approach to solving linear-nonlinear FDEs by advantageously creating a functional series solution, initially presented by Adomian [48]. Later, this approach was used with numerous transformations (such as the Sumudu, Aboodh, Laplace, and Mohand transforms), as shown in [49][50][51][52][53][54][55][56][57][58].…”

Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

“…Various innovators established the underlying framework, as well as their perspectives on expanding calculus, including Liouville, Hadamard, Caputo, Grunwald, Letnikov, Abel, Riez, Caputo-Fabrizio, Atangana-Baleanu (AB), who researched the use of the fractional derivative and fractional differential equations (FDEs). Numerous essential interactions in electromagnetics, acoustics, viscoelasticity, electrochemistry, and material science are well explained by FDEs [8][9][10][11][12][13][14][15][16][17][18][19][20].…”