EXISTENCE OF SOLUTIONS FOR A CONTINUOUS MULTIGRAIN MODEL  FOR POLYMERIZATION

We prove the existence and uniqueness of solutions, for small times, for a mathematical scheme modeling the Ziegler–Natta process of polymerization. The model consists, essentially, of two diffusion problems at two different space scales, one relative to the microscopical catalyst pellets, the other to the macroscopical aggregate of those pellets. The coupling between the two scales is of nonstandard nature.

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Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽

10.3390/sym13081431 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1431

Author(s):

Bilal Basti ◽

Nacereddine Hammami ◽

Imadeddine Berrabah ◽

Farid Nouioua ◽

Rabah Djemiat ◽

...

Keyword(s):

Mathematical Model ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Fixed Point Theorems ◽

Existence Of Solutions ◽

Biological Models ◽

Uniqueness Of Solutions ◽

Caputo Fractional Derivatives ◽

Single Form ◽

Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

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On the existence of solutions of strongly damped nonlinear wave equations

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171200000971 ◽

2000 ◽

Vol 23 (6) ◽

pp. 369-382 ◽

Cited By ~ 6

Author(s):

Jong Yeoul Park ◽

Jeong Ja Bae

Keyword(s):

Nonlinear Wave ◽

Existence And Uniqueness ◽

Wave Equations ◽

Existence Of Solutions ◽

Hyperbolic Type ◽

Nonlinear Wave Equations ◽

Gamma Delta ◽

Uniqueness Of Solutions ◽

Alpha Beta ◽

Strongly Damped

We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation:utt(t,x)−(α+β(∫Ω|∇u(t,y)|2dy)γ)Δu(t,x) −λΔut(t,x)+μ|u(t,x)|q−1u(t,x)=0, x∈Ω,t≥0 u(0,x)=u0(x), ut(0,x)=u1(x), x∈Ω, u|∂Ω=0, whereq>1,λ>0,μ∈ℝ,α,β≥0,α+β>0, andΔis the Laplacian inℝN.

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Existence of Solutions ofα∈(2,3]Order Fractional Three-Point Boundary Value Problems with Integral Conditions

Abstract and Applied Analysis ◽

10.1155/2014/198632 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

N. I. Mahmudov ◽

S. Unul

Keyword(s):

Fixed Point ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Fixed Point Theorems ◽

Existence Of Solutions ◽

Point Boundary ◽

Integral Conditions ◽

Uniqueness Of Solutions ◽

Fractional Differential ◽

Derivatives Of

Existence and uniqueness of solutions forα∈(2,3]order fractional differential equations with three-point fractional boundary and integral conditions involving the nonlinearity depending on the fractional derivatives of the unknown function are discussed. The results are obtained by using fixed point theorems. Two examples are given to illustrate the results.

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Existence and uniqueness of solutions to a concentrated capacity problem with change of phase

European Journal of Applied Mathematics ◽

10.1017/s0956792500000280 ◽

1990 ◽

Vol 1 (4) ◽

pp. 339-351 ◽

Cited By ~ 9

Author(s):

Daniele Andreucci

Keyword(s):

Heat Equation ◽

Existence And Uniqueness ◽

Continuous Dependence ◽

Weak Sense ◽

Uniqueness Of Solutions ◽

Limiting Case ◽

Multidimensional Domain ◽

Diffusion Problems

A concentrated capacity problem is posed for the heat equation in a multidimensional domain. In the concentrated capacity (i.e. in a portion of the boundary of the domain) a change of phase takes place, and a Stefan-like problem is posed. This scheme has been introduced in the literature as the formal limiting case of a certain class of diffusion problems.Our main result is a theorem of continuous dependence of the solution on the data. It is also used to prove the existence of the solution (in a weak sense), assuming only integrability of the data. The solution is found as the limit of the solutions of the approximating problems.

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System of fractional differential equations with Erdélyi-Kober fractional integral conditions

Open Mathematics ◽

10.1515/math-2015-0079 ◽

2015 ◽

Vol 13 (1) ◽

Cited By ~ 1

Author(s):

Natthaphong Thongsalee ◽

Sorasak Laoprasittichok ◽

Sotiris K. Ntouyas ◽

Jessada Tariboon

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fractional Integral ◽

Existence Of Solutions ◽

Integral Conditions ◽

Liouville Type ◽

Uniqueness Of Solutions ◽

Fractional Differential ◽

Banach’S Contraction Principle

AbstractIn this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.

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Heterogeneous Diffusion, Stability Analysis, and Solution Profiles for a MHD Darcy–Forchheimer Model

Mathematics ◽

10.3390/math10010020 ◽

2021 ◽

Vol 10 (1) ◽

pp. 20

Author(s):

José Luis Díaz ◽

Saeed Rahman ◽

Juan Miguel García-Haro

Keyword(s):

Stability Analysis ◽

Existence And Uniqueness ◽

Stability Study ◽

The Other ◽

Spatial Structures ◽

Spatial Derivative ◽

Uniqueness Of Solutions ◽

Forchheimer Model ◽

Inner Region ◽

Forchheimer Flow

In the presented analysis, a heterogeneous diffusion is introduced to a magnetohydrodynamics (MHD) Darcy–Forchheimer flow, leading to an extended Darcy–Forchheimer model. The introduction of a generalized diffusion was proposed by Cohen and Murray to study the energy gradients in spatial structures. In addition, Peletier and Troy, on one side, and Rottschäfer and Doelman, on the other side, have introduced a general diffusion (of a fourth-order spatial derivative) to study the oscillatory patterns close the critical points induced by the reaction term. In the presented study, analytical conceptions to a proposed problem with heterogeneous diffusions are introduced. First, the existence and uniqueness of solutions are provided. Afterwards, a stability study is presented aiming to characterize the asymptotic convergent condition for oscillatory patterns. Dedicated solution profiles are explored, making use of a Hamilton–Jacobi type of equation. The existence of oscillatory patterns may induce solutions to be negative, close to the null equilibrium; hence, a precise inner region of positive solutions is obtained.

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New Existence of Solutions for Fractional Integro-Differential Equations with Nonseparated Boundary Conditions

Mathematical Problems in Engineering ◽

10.1155/2021/9915375 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Lahcen Ibnelazyz ◽

Karim Guida ◽

Khalid Hilal ◽

Said Melliani

Keyword(s):

Differential Equations ◽

Existence And Uniqueness ◽

Contraction Mapping ◽

Existence Of Solutions ◽

Contraction Mapping Principle ◽

Existence Of Solution ◽

Uniqueness Of Solutions ◽

Uniqueness Results ◽

Nonseparated Boundary Conditions ◽

Krasnoselskii Fixed Point Theorem

Results reported in this article prove the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations supplemented by nonseparated boundary value conditions. We consider a new norm to establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle. Some examples are provided to illustrate the results.

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Uniqueness and existence of solutions for nonlinear fractional differential equations with two fractional orders

Mathematica ◽

10.24193/mathcluj.2021.2.11 ◽

2021 ◽

Vol 63 (86) (2) ◽

pp. 254-267

Author(s):

Mohamed Houas ◽

◽

Zoubir Dahmani ◽

Erhan Set ◽

◽

...

Keyword(s):

Differential Equations ◽

Existence And Uniqueness ◽

Existence Of Solutions ◽

Degree Theory ◽

Uniqueness Of Solutions ◽

Nonlinear Alternative ◽

Banach’S Fixed Point Theorem ◽

Fractional Differential ◽

Uniqueness And Existence ◽

Fractional Orders

We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.

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