Results 1 to 10 of about 831 (128)

A generalized Picard-Lindelöf theorem [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2016
We generalize the Picard-Lindelöf theorem on the unique solvability of initial value problems $\dot x=f(t,x)$, $x(t_0)=x_0$, by replacing the sufficient classical Lipschitz condition of $f$ with respect to $x$ with a more general Lipschitz condition ...
Stefan Siegmund, Christine Nowak, Josef Diblik   +2 more
doaj   +6 more sources

Mathematical modeling of allelopathic stimulatory phytoplankton species using fractal–fractional derivatives [PDF]

Scientific Reports
In the current study, we employ the novel fractal–fractional operator in the Atangana–Baleanu sense to investigate the dynamics of an interacting phytoplankton species model.
Sangeeta Kumawat, Sanjay Bhatter, Bhamini Bhatia, Sunil Dutt Purohit, D. L. Suthar   +4 more
doaj   +2 more sources

Mathematical model of the lumpy skin disease using Caputo fractional-order derivative via invariant point technique [PDF]

Scientific Reports
The aim of this paper is to study the fractional model of Lumpy Skin Disease, aiming to enhance our understanding of this disease. Specifically, we employ the recently introduced Caputo–Fabrizio fractional (CFF) derivative to analyze the Lumpy Skin ...
Gunaseelan Mani, Arul Joseph Gnanaprakasam, Sakthi Ramalingam, Abdoalrahman S. A. Omer, Ilyas Khan   +4 more
doaj   +2 more sources

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach [PDF]

Results in Physics, 2022
Super-spreaders of the novel coronavirus disease (or COVID-19) are those with greater potential for disease transmission to infect other people. Understanding and isolating the super-spreaders are important for controlling the COVID-19 incidence as well ...
Xiao-Ping Li, Saif Ullah, Hina Zahir, Ahmed Alshehri, Muhammad Bilal Riaz, Basem Al Alwan   +5 more
doaj   +2 more sources

Optimal version of the Picard–Lindelöf theorem

Electronic Journal of Qualitative Theory of Differential Equations, 2021
Consider the differential equation $y'=F(x,y)$. We determine the weakest possible upper bound on $|F(x,y)-F(x,z)|$ which guarantees that this equation has for all initial values a unique solution, which exists globally.
Jan-Christoph Schlage-Puchta
doaj   +1 more source

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

Mathematics, 2021
In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon.
Samad Noeiaghdam, Sanda Micula, Juan J. Nieto   +2 more
doaj   +1 more source

An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

Journal of Function Spaces, 2021
In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative.
H. R. Marasi, A. Soltani Joujehi, H. Aydi   +2 more
doaj   +1 more source

Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method

Abstract and Applied Analysis, 2022
The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution.
Mohammed Hirpho
doaj   +1 more source

A mathematical model for simulating the transmission dynamics of COVID-19 using the Caputo–Fabrizio fractional-order derivative with nonsingular kernel

Informatics in Medicine Unlocked, 2023
The emergence of the new coronavirus variant from the coronaviridae family has become a global concern, and all nations, including Bangladesh, are battling to contain the spread of the disease.
Anip Kumar Paul, Neerob Basak, Md Abdul Kuddus   +2 more
doaj   +1 more source

Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator

Results in Control and Optimization, 2023
The aim of this paper is to analyze a fractional model of the Ebola virus. This study is important because it contributes to our understanding of the Ebola virus transmission dynamics using the notion of non-local differential operators.
Pooja Yadav, Shah Jahan, Kottakkaran Sooppy Nisar   +2 more
doaj   +1 more source