Titlebook: Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization; Said Melliani,Oscar Castillo Conference proce

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Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization978-3-031-12416-7Series ISSN 2367-3370 Series E-ISSN 2367-3389

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A SIR Epedimic Model Involving Fractional Atangana Derivative,This paper aime to analyzes a fractional order SIR epidemic model with a nonlinear incidence rate. First, we prove the global existence, positivity and boundedness of the solutions. The stability is studied. Finally, numerical simulations are presented to illustrate our theoretical results.

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Fuzzy Local Ring,In this work we define a fuzzy divisible ring and fuzzy local ring using the notion of fuzzy point, Also we give a characterization of fuzzy local rings.

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,Gevrey Class Regularity for the 2D Subcritical Dissipative Quasi-geostrophic Equation in Critical FThe dissipative two dimensional Quasi-Geostrophic Equation (2D QGE) is studied. By using the Littlewood Paley theory, Fourier analysis and standard techniques we give the Gevrey class regularity results of this equation for small initial data . belonging to the critical Fourier-Besov-Morrey spaces ..

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,Notes on the Existence Results for Nonlinear Fractional Differential Equations with Fuzzy Boundary In this paper, we establish a new result concerning the existence and uniqueness of solutions for nonlinear fractional differential equations with fuzzy boundary conditions. As application, we give an illustrative example to show the effectiveness of the obtained result.

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,Generalized Solution of Transport Equation,In this paper we proved some importance proprieties of Colombeau algebra, we proved the existence and uniqueness of solution of transport equation with variable speed and initial data in the Colombeau algebra .. We proved the association of the generalized solution with the classical solution.

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,Generalized Solution of Non-homogeneous Wave Equation,In this paper, we are interested to study the non-homogeneous wave equation in generalized function algebra, we give a result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.

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