Browsing by Author "Ahmed, Idris"

Now showing 1 - 7 of 7

Citation - WoS: 7
Analysis O a Caputo Hiv and Malaria Co-Infection Epidemic Model
(Chiang Mai Univ, Fac Science, 2021) Ahmed, Idris; Jarad, Fahd; Yusuf, Abdullahi; Sani, Musbahu Aminu; Jarad, Fahd; Kumam, Wiyada; Thounthong, Phatiphat; Matematik
In this paper, we investigate a fractional-order compartmental HIV and Malaria co-infection epidemic model using the Caputo derivative. The existence and uniqueness of the solution to the proposed fractional-order model were investigated using fixed point theorem techniques. To demonstrate that the proposed fractional-order model is both mathematically and epidemiologically well-posed, we compute the model's positivity and boundedness, which is an important feature in epidemiology. Finally, we analyze the dynamic behavior of each of the state variables using a recent and powerful computational technique known as the fractional Euler method.
Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition
(2020) Ahmed, Idris; Kumam, Poom; Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained. © 2020, The Author(s).
Citation - WoS: 10
Citation - Scopus: 13
Existence and Uniqueness Results for Φ-Caputo Implicit Fractional Pantograph Differential Equation With Generalized Anti-Periodic Boundary Condition
(Springer, 2020) Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; Ahmed, Idris; Kumam, Poom
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green's function of the proposed problems. With the aid of a Green's function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.
Citation - WoS: 7
Citation - Scopus: 8
Numerical and Theoretical Analysis of an Awareness Covid-19 Epidemic Model Via Generalized Atangana-Baleanu Fractional Derivative
(Czestochowa Univ Technology, inst Mathematics, 2022) Ahmed, Idris; Al-Mdallal, Qasem M.; Jarad, Fahd; Yunusa, Salisu; Baba, Isa Abdullahi
In this paper, a COVID-19 Awareness model in the setting of a generalized fractional Atangana-Baleanu derivative is proposed. The existence and uniqueness of a solution of the proposed fractional-order model are investigated under the techniques of fixed point theorems. In addition, we perform the predictor-corrector method to find its numeric solutions and present the graphs of the various solutions using different values of the parameters embodied in the derivative.
Citation - WoS: 56
Citation - Scopus: 67
On Hilfer Generalized Proportional Fractional Derivative
(Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; Ahmed, Idris
Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
Citation - WoS: 30
On Ψ-Hilfer Generalized Proportional Fractional Operators
(Amer inst Mathematical Sciences-aims, 2021) Ahmed, Idris; Akgul, Ali; Jarad, Fahd; Alha, Subhash; Mallah, Ishfaq
In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the psi-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.
Citation - WoS: 31
Citation - Scopus: 29
Stability Analysis for Boundary Value Problems With Generalized Nonlocal Condition Via Hilfer-Katugampola Fractional Derivative
(Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Sitthithakerngkiet, Kanokwan; Ibrahim, Alhassan; Ahmed, Idris
In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville-Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii's fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.