scholarly journals ANALYSIS OF FRACTAL–FRACTIONAL MALARIA TRANSMISSION MODEL

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040041 ◽  
Author(s):  
J. F. GÓMEZ-AGUILAR ◽  
T. CÓRDOVA-FRAGA ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN ◽  
HASIB KHAN
Keyword(s):  
Malaria Transmission ◽  
Exponential Decay ◽  
Power Law ◽  
Fixed Point Theory ◽  
Control Strategies ◽  
Point Theory ◽  
Transmission Model ◽  
Fractional Operators ◽  
Uniqueness And Existence ◽  
Exponential Decay Law

In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives [Formula: see text] and [Formula: see text].

scholarly journals Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel

2022 ◽  
Vol 7 (1) ◽  
pp. 756-783
Author(s):  
Muhammad Farman ◽  
◽  
Ali Akgül ◽  
Kottakkaran Sooppy Nisar ◽  
Dilshad Ahmad ◽  
...  
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Control Strategies ◽  
Point Theory ◽  
Fractional Operators ◽  
Order Model ◽  
Epidemiological Analysis ◽  
Fractional Order Model ◽  
Sumudu Transform

<abstract> <p>This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies.</p> </abstract>

scholarly journals Novel Fractional Operators with Three Orders and Power-Law, Exponential Decay and Mittag–Leffler Memories Involving the Truncated M-Derivative

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 626 ◽  
Author(s):  
Jesús Emmanuel Solís-Pérez ◽  
José Francisco Gómez-Aguilar
Keyword(s):  
Numerical Analysis ◽  
Exponential Decay ◽  
Power Law ◽  
Chaotic Attractor ◽  
Lagrange Interpolation ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
Fractional Operators ◽  
Conformable Derivative ◽  
Sensitive Dependence

In this research, novel M-truncated fractional derivatives with three orders have been proposed. These operators involve truncated Mittag–Leffler function to generalize the Khalil conformable derivative as well as the M-derivative. The new operators proposed are the convolution of truncated M-derivative with a power law, exponential decay and the complete Mittag–Leffler function. Numerical schemes based on Lagrange interpolation to predict chaotic behaviors of Rucklidge, Shimizu–Morioka and a hybrid strange attractors were considered. Additionally, numerical analysis based on 0–1 test and sensitive dependence on initial conditions were carried out to verify and show the existence of chaos in the chaotic attractor. These results showed that these novel operators involving three orders, two for the truncated M-derivative and one for the fractional term, depict complex chaotic behaviors.

scholarly journals Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Choonkil Park ◽  
Manuel de la Sen ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
New Type ◽  
Uniqueness And Existence

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U -contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equations.

scholarly journals A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi
Keyword(s):  
Fractional Order ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Point Theory ◽  
Euler Method ◽  
Transmission Model ◽  
Order Model ◽  
Influenza Transmission ◽  
The Stability ◽  
Disease Free

Abstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.

scholarly journals Mathematical Modeling and Forecasting of COVID-19 in Saudi Arabia under Fractal-Fractional Derivative in Caputo Sense with Power-Law

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 228
Author(s):  
Mdi Begum Jeelani ◽  
Abeer S. Alnahdi ◽  
Mohammed S. Abdo ◽  
Mansour A. Abdulwasaa ◽  
Kamal Shah ◽  
...  
Keyword(s):  
Saudi Arabia ◽  
Fractional Order ◽  
Power Law ◽  
Reproduction Number ◽  
Fixed Point Theory ◽  
Fractal Dimensions ◽  
Real Data ◽  
Point Theory ◽  
Modeling And Forecasting ◽  
Uniqueness Of The Solution

This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order μ and fractal dimension χ. We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.

scholarly journals On modeling of coronavirus-19 disease under Mittag-Leffler power law

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Samia Bushnaq ◽  
Kamal Shah ◽  
Hussam Alrabaiah
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Fractional Order ◽  
Power Law ◽  
Fixed Point Theory ◽  
Numerical Technique ◽  
Approximate Solutions ◽  
Point Theory ◽  
New Model

Abstract This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as $(\mathcal{ABC})$ ( ABC ) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

scholarly journals ATANGANA–SEDA NUMERICAL SCHEME FOR LABYRINTH ATTRACTOR WITH NEW DIFFERENTIAL AND INTEGRAL OPERATORS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040044
Author(s):  
ABDON ATANGANA ◽  
SEDA İĞRET ARAZ
Keyword(s):  
Numerical Simulations ◽  
Exponential Decay ◽  
Power Law ◽  
Real World ◽  
Numerical Scheme ◽  
Integral Operators ◽  
Fractional Operators ◽  
Mathematical Concepts ◽  
Newton Polynomial ◽  
Real World Problems

In this paper, we present a new numerical scheme for a model involving new mathematical concepts that are of great importance for interpreting and examining real world problems. Firstly, we handle a Labyrinth chaotic problem with fractional operators which include exponential decay, power-law and Mittag-Leffler kernel. Moreover, this problem is solved via Atangana-Seda numerical scheme which is based on Newton polynomial. The accuracy and efficiency of the method can be easily seen with numerical simulations.

scholarly journals CAUCHY PROBLEMS WITH FRACTAL–FRACTIONAL OPERATORS AND APPLICATIONS TO GROUNDWATER DYNAMICS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040043 ◽  
Author(s):  
ABDON ATANGANA ◽  
EMILE FRANC DOUNGMO GOUFO
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Exponential Decay ◽  
Power Law ◽  
Differential Operators ◽  
Cauchy Problems ◽  
Partial Differential ◽  
Liouville Derivative ◽  
Exponential Decay Law ◽  
The Impact

As the Riemann–Liouville derivative is a derivative of a convolution of a function and the power law, the fractal–fractional derivative of a function is the fractal derivative of a convolution of that function with the power law or exponential decay. In order to further open new doors on ongoing investigations with field of partial differential equations with non-conventional differential operators, we introduce in this paper new Cauchy problems with fractal–fractional differential operators. We consider two cases, when the operator is constructed with power law and when it is constructed with exponential decay law with Delta-Dirac property. For each case, we present the conditions under which the exact solution exists and is unique. We suggest a suitable and accurate numerical scheme that can be used to solve such differential equation numerically. We present illustrative examples where an application to a partial differential equation and to a model of groundwater flow within the confined aquifer are done with numerical simulations provided. The clear variation of water level shows the impact of the fractal–fractional derivative on the dynamics.

scholarly journals Hyers–Ulam stability of non-autonomous and nonsingular delay difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Gul Rahmat ◽  
Atta Ullah ◽  
Aziz Ur Rahman ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad ◽  
...  
Keyword(s):  
Fixed Point Theory ◽  
Theoretical Work ◽  
Point Theory ◽  
Ulam Stability ◽  
Delay Difference Equation ◽  
Discrete Interval ◽  
Uniqueness And Existence ◽  
The Given ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper, we study the uniqueness and existence of the solution of a non-autonomous and nonsingular delay difference equation using the well-known principle of contraction from fixed point theory. Furthermore, we study the Hyers–Ulam stability of the given system on a bounded discrete interval and then on an unbounded interval. An example is also given at the end to illustrate the theoretical work.

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