scholarly journals Local existence and uniqueness for a fractional SIRS model with Mittag–Leffler law

2021 ◽  
Vol 10 (2) ◽  
pp. 61-71
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri ◽  
Delfim F. M. Torres
Keyword(s):  
Existence And Uniqueness ◽  
Iterative Scheme ◽  
Local Existence ◽  
Special Solution ◽  
Banach Fixed Point Theorem ◽  
Existence Of A Solution ◽  
Local Existence And Uniqueness ◽  
Sirs Model ◽  
Uniqueness And Existence ◽  
The Stability

In this paper, we study an epidemic model with Atangana-Baleanu-Caputo fractional derivative. We obtain a special solution using an iterative scheme via Laplace transformation. Uniqueness and existence of a solution using the Banach fixed point theorem are studied. A detailed analysis of the stability of the special solution is presented. Finally, our generalized model in the derivative sense is solved numerically by the Adams-Bashforth-Moulton method.

scholarly journals A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Existence And Uniqueness ◽  
Laplace Transformation ◽  
Cell Phones ◽  
Mobile Network ◽  
The Other ◽  
Banach Fixed Point Theorem ◽  
Propagation Models ◽  
Computer Worms ◽  
Computer Viruses ◽  
The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

GENESIS OF A SOURCE/SINK LINE INTO A SINGULAR UPDRAFT

1998 ◽  
Vol 08 (03) ◽  
pp. 431-444 ◽  
Author(s):  
JOËL CHASKALOVIC
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Vortex Line ◽  
Stokes Equations ◽  
Local Existence ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Existence And Uniqueness ◽  
Source Sink

Mathematical models applied to tornadoes describe these kinds of flows as an axisymmetric fluid motion which is restricted for not developing a source or a sink near the vortex line. Here, we propose the genesis of a family of a source/sink line into a singular updraft which can modeled one of the step of the genesis of a tornado. This model consists of a three-parameter family of fluid motions, satisfying the steady and incompressible Navier–Stokes equations, which vanish at the ground. We establish the local existence and uniqueness for these fields, at the neighborhood of a nonrotating singular updraft.

scholarly journals ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING

2009 ◽  
Vol 09 (03) ◽  
pp. 437-477 ◽  
Author(s):  
AURÉLIEN DEYA ◽  
SAMY TINDEL
Keyword(s):  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Volterra Equations ◽  
Existence And Uniqueness Theorem ◽  
Hölder Exponent ◽  
Local Existence And Uniqueness ◽  
Hurst Coefficient ◽  
Rough Path ◽  
Driving Signal

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ < 1/2, we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H > 1/3.

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