Mohammad, Mutaz Trounev, Alexander
Published in
Chaos, solitons, and fractals
In this paper, we present a novel fractional order COVID-19 mathematical model by involving fractional order with specific parameters. The new fractional model is based on the well-known Atangana-Baleanu fractional derivative with non-singular kernel. The proposed system is developed using eight fractional-order nonlinear differential equations. Th...
Zhang, Zizhen Zeb, Anwar Egbelowo, Oluwaseun Francis Erturk, Vedat Suat
Published in
Advances in Difference Equations
In this work, we formulate and analyze a new mathematical model for COVID-19 epidemic with isolated class in fractional order. This model is described by a system of fractional-order differential equations model and includes five classes, namely, S (susceptible class), E (exposed class), I (infected class), Q (isolated class), and R (recovered clas...
Liu, Hui Li, Yongjin
Published in
Advances in Difference Equations
Motivated by Shen et al., we apply the Gronwall’s inequality to establish the Hyers–Ulam stability of two types (Riemann–Liouville and Caputo) of linear fractional differential equations with variable coefficients under certain conditions.
Fernandez, Arran Kürt, Cemaliye Özarslan, Mehmet Ali
Published in
Computational and Applied Mathematics
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional integral operator which has many interesting properties. The motivation for these definitions is twofold: firs...
Mohammad, Mutaz Trounev, Alexander
Published in
Chaos, Solitons, and Fractals
Riesz wavelets in L 2 ( R ) have been proven as a useful tool in the context of both pure and numerical analysis in many applications, due to their well prevailing and recognized theory and its natural properties such as sparsity and stability which lead to a well-conditioned scheme. In this paper, an effective and accurate technique based on Riesz...
Rambour, Philippe Seghier, Abdellatif
Toeplitz matrices for the study of the fractional Laplacian on a bounded interval. In this work we get a deep link between (−∆) α ]0,1[ the fractional Laplacian on the interval ]0, 1[ and T N (ϕ α) the Toeplitz matrices of symbol ϕ α : θ → |1 − e iθ | 2α when N goes to the infinity and for α ∈]0, 1 2 [∪] 1 2 , 1[. In the second part of the paper we...
Lorin, E.
Published in
Advances in Difference Equations
This paper is dedicated to the derivation of a simple parallel in space and time algorithm for space and time fractional evolution partial differential equations. We report the stability, the order of the method and provide some illustrating numerical experiments.
Ferrari, Alberto José Lara, Luis Pedro Santillan Marcus, Eduardo Adrian
Published in
Journal of the Egyptian Mathematical Society
In this study, a new form of a quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve integral equations.
Li, Shuai Zhang, Zhixin Jiang, Wei
Published in
Advances in Difference Equations
In this article, a class of integral boundary value problems of fractional delayed differential equations is discussed. Based on the Guo–Krasnoselskii theorem, some existence results on the positive solutions are derived. Two simple examples are given to show the validity of the conditions of our main theorems.
Betancur-Herrera, David E Muñoz-Galeano, Nicolas
Published in
Data in brief
The data presented in this paper are related to the paper entitled "A Numerical Method for Solving Caputo's and Riemann-Liouville's Fractional Differential Equations which includes multi-order fractional derivatives and variable coefficients", available in the "Communications in Nonlinear Science and Numerical Simulation" journal. Here, data are in...
