Browsing by Author "Ahmad, Abdulaziz Garba"

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Citation - WoS: 23
Citation - Scopus: 26
A novel fractal-fractional order model for the understanding of an oscillatory and complex behavior of human liver with non-singular kernel
(Elsevier, 2022) Rashid, Saima; Jarad, Fahd; Jarad, Fahd; Ahmad, Abdulaziz Garba; 234808; Matematik
Scientists and researchers are increasingly interested in numerical simulations of infections with non-integer orders. It is self-evident that conventional epidemiological systems can be given in a predetermined order, but fractional-order derivative systems are not stable orders. The fractional derivative proves increasingly effective in representing real-world issues when it has a non-fixed order. Various novel fractional operator notions, including special functions in the kernel, have been presented in recent decades, which transcend the constraints of prior fractional order derivatives. These novel operators have been shown to be useful in simulating scientific and technical challenges. The fractal-fractional operator is a relatively modern fractional calculus operator that has been proposed. Besides that, we propose a new technique and implement it in a human liver model and want to investigate its dynamics. In the context of this novel operator, we demonstrate certain interesting findings for the human liver model. The findings of the uniqueness and existence will be revealed. We describe modeling estimates for the proposed model using an innovative numerical method that has never been used before for a human liver model of this type. Additionally, graphical illustrations are demonstrated for both fractal and fractional orders. It is expected that the fractal-fractional approach is more invigorating and effective for epidemic models than the fractional operator.
Citation - WoS: 16
Citation - Scopus: 21
New numerical dynamics of the heroin epidemic model using a fractional derivative with Mittag-Leffler kernel and consequences for control mechanisms
(Elsevier, 2022) Rashid, Saima; Jarad, Fahd; Jarad, Fahd; Ahmad, Abdulaziz Garba; Abualnaja, Khadijah M.; 234808; Matematik
Intravenous substance consumption is on the upswing all over the globe, especially in Europe and Asia. It is extremely harmful to society; excessive substance consumption is the leading cause of death. Beyond all prohibited narcotics, heroin is a narcotic that has a substantial negative impact on society and the world at large. In this paper, a heroin epidemic model is developed via an Atangana-Baleanu fractional-order derivative in the Caputo sense describe accurately real world problems, equipped with recovery and persistent immunity. Meanwhile, we have established a globally asymptotically stable equilibrium for both the drug-free and drug-addiction equilibriums. Additionally, we apply a novel scheme that is mingled with the two-step Lagrange polynomial and the basic principle of fractional calculus. The simulation results for various fractional values indicate that as the fractional order decreases from 1, the growth of the epidemic diminishes. The modelling data demonstrates that the suggested containment technique is effective in minimizing the incidence of instances in various categories. Furthermore, modelling the ideal configuration indicated that lowering the fractional-order from 1 necessitates a swift commencement of the implementation of the suggested regulatory technique at the maximum rate and sustaining it throughout a significant proportion of the pandemic time frame.
Citation - WoS: 5
Citation - Scopus: 3
Nonlinear fractional differential equations and their existence via fixed point theory concerning to Hilfer generalized proportional fractional derivative
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Ahmad, Abdulaziz Garba; Jarad, Fahd; Alsaadi, Ateq; 234808; Matematik
This article adopts a class of nonlinear fractional differential equation associating Hilfer generalized proportional fractional (GPF) derivative with having boundary conditions, which amalgamates the Riemann-Liouville (RL) and Caputo-GPF derivative. Taking into consideration the weighted space continuous mappings, we first derive a corresponding integral for the specified boundary value problem. Also, we investigate the existence consequences for a certain problem with a new unified formulation considering the minimal suppositions on nonlinear mapping. Detailed developments hold in the analysis and are dependent on diverse tools involving Schauder's, Schaefer's and Kransnoselskii's fixed point theorems. Finally, we deliver two examples to check the efficiency of the proposed scheme.