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

• Published in: Fractal and fractional Vol. 5; no. 3; p. 94
• Main Authors: Rashid, Saima, Hammouch, Zakia, Aydi, Hassen, Ahmad, Abdulaziz Garba, Alsharif, Abdullah M.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-09-2021
• Subjects: AB-fractional operator; Caputo fractional derivative; Decomposition; Elzaki transform; Epidemics; Fisher’s equation; Fixed points (mathematics); Fractional calculus; Iterative methods; new iterative transform method; Operators (mathematics); Robustness (mathematics)
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract5030094

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.