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

Symmetry ◽  
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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
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.

scholarly journals Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. M. Matar ◽  
M. I. Abbas ◽  
J. Alzabut ◽  
M. K. A. Kaabar ◽  
S. Etemad ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives

AbstractA newly proposed p-Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem using some fixed point theorems such as Banach and Schauder. This work is supported with an example to apply all obtained new results and validate their applicability.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

scholarly journals Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Arshad Ali ◽  
Vidushi Gupta ◽  
Thabet Abdeljawad ◽  
Kamal Shah ◽  
Fahd Jarad
Keyword(s):  
Boundary Conditions ◽  
Mathematical Analysis ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Boundary Conditions ◽  
Stability Results ◽  
Rassias Stability

This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).

scholarly journals On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed S. Abdo ◽  
Thabet Abdeljawad ◽  
Saeed M. Ali ◽  
Kamal Shah
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Conditions ◽  
Caputo Fractional Derivatives ◽  
Derivatives Of ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of orders $0<\vartheta \leq 1$ 0 < ϑ ≤ 1 and $1<\vartheta \leq 2$ 1 < ϑ ≤ 2 . We structure the equivalent fractional integral equations of the proposed problems. Further, the existence and uniqueness theorems are proved with the aid of fixed point theorems of Krasnoselskii and Banach. Lastly, the paper includes pertinent examples to justify the validity of the results.

scholarly journals Existence Results for a Nonlocal Coupled System of Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 578
Author(s):  
Sotiris K. Ntouyas ◽  
Abrar Broom ◽  
Ahmed Alsaedi ◽  
Tareq Saeed ◽  
Bashir Ahmad
Keyword(s):  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Uniqueness Result ◽  
Existence Results ◽  
System Of Differential Equations ◽  
Liouville Type ◽  
Uniqueness Of Solutions ◽  
Fractional Derivatives And Integrals

In this paper, we study the existence and uniqueness of solutions for a new kind of nonlocal four-point fractional integro-differential system involving both left Caputo and right Riemann–Liouville fractional derivatives, and Riemann–Liouville type mixed integrals. The Banach and Schaefer fixed point theorems are used to obtain the desired results. An example illustrating the existence and uniqueness result is presented.

scholarly journals Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Intuitionistic Fuzzy ◽  
Uniqueness Results ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.

scholarly journals Existence Theorems for Mixed Riemann–Liouville and Caputo Fractional Differential Equations and Inclusions with Nonlocal Fractional Integro-Differential Boundary Conditions

2019 ◽  
Vol 3 (2) ◽  
pp. 21 ◽  
Author(s):  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Existence Theorems ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
New Class ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

In this paper, we discuss the existence and uniqueness of solutions for a new class of single and multi-valued boundary value problems involving both Riemann–Liouville and Caputo fractional derivatives, and nonlocal fractional integro-differential boundary conditions. Our results rely on modern tools of functional analysis. We also demonstrate the application of the obtained results with the aid of examples.

Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zohre Kiyamehr ◽  
Hamid Baghani
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Langevin Equations ◽  
Point Boundary ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThis article investigates a nonlinear fractional Caputo–Langevin equationD^{\beta}(D^{\alpha}+\lambda)x(t)=f(t,x(t)),\quad 0<t<1,\,0<\alpha\leq 1,\,1<% \beta\leq 2,subject to the multi-point boundary conditionsx(0)=0,\qquad\mathcal{D}^{2\alpha}x(1)+\lambda\mathcal{D^{\alpha}}x(1)=0,% \qquad x(1)=\int_{0}^{\eta}x(\tau)\,d\tau\quad\text{for some }0<\eta<1,where {D^{\alpha}} is the Caputo fractional derivative of order α, {f:[0,1]\times\mathbb{R}\to\mathbb{R}} is a given continuous function, and λ is a real number. Some new existence and uniqueness results are obtained by applying an interesting fixed point theorem.

scholarly journals Coupled implicit Caputo fractional q-difference systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Bessem Samet ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Difference System ◽  
Uniqueness Of Solutions ◽  
Difference Systems ◽  
Stability Results

AbstractThis paper deals with some existence, uniqueness, and Ulam stability results for a coupled implicit Caputo fractional q-difference system in Banach and generalized Banach spaces. Some applications are made of some fixed point theorems for the existence and uniqueness of solutions. Next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Some illustrative examples are given in the last section.

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