Browsing by Author "Akgul, Ali"

Now showing 1 - 20 of 48

Citation - WoS: 31
Citation - Scopus: 35
Analysis and Applications of the Proportional Caputo Derivative
(Springer, 2021) Baleanu, Dumitru; Akgul, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we investigate the analysis of the proportional Caputo derivative that recently has been constructed. We create some useful relations between this new derivative and beta function. We discretize the new derivative. We investigate the stability and obtain a stability condition for the new derivative.
Citation - WoS: 23
Citation - Scopus: 28
Analysis of a Fractional Order Bovine Brucellosis Disease Model With Discrete Generalized Mittag-Leffler Kernels
(Elsevier, 2023) Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; Attia, Nourhane; Hassan, Ahmed M.; Farman, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness's increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana-Baleanu fractional difference operator of the Liouville-Caputo type. An analysis of the suggested system's well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.
Citation - WoS: 33
Citation - Scopus: 36
Analysis of Fractional Order Chaotic Financial Model With Minimum Interest Rate Impact
(Mdpi, 2020) Akgul, Ali; Baleanu, Dumitru; Imtiaz, Sumaiyah; Ahmad, Aqeel; Farman, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main objective of this paper is to construct and test fractional order derivatives for the management and simulation of a fractional order disorderly finance system. In the developed system, we add the critical minimum interest ratedparameter in order to develop a new stable financial model. The new emerging paradigm increases the demand for innovation, which is the gateway to the knowledge economy. The derivatives are characterized in the Caputo fractional order derivative and Atangana-Baleanu derivative. We prove the existence and uniqueness of the solutions with fixed point theorem and an iterative scheme. The interest rate begins to rise according to initial conditions as investment demand and price exponent begin to fall, which shows the financial system's actual macroeconomic behavior. Specifically component of its application to the large scale and smaller scale forms, just as the utilization of specific strategies and instruments such fractal stochastic procedures and expectation.
Citation - WoS: 9
Citation - Scopus: 9
Analysis of Hiv/Aids Model With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2022) Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, Fahd; Akram, Muhammad Mannan; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.
Citation - WoS: 14
Citation - Scopus: 16
Analysis of the Fractional Diarrhea Model With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2022) Iqbal, Muhammad Sajid; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Shahzad, Muhammad; Iqbal, Zafar; Jarad, Fahd; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R-0 and some concluding remarks.
Citation - WoS: 43
Citation - Scopus: 49
Analysis of the Fractional Tumour-Immune Model With Mittag-Leffler Kernel
(Elsevier, 2020) Ullah, Aman; Akgul, Ali; Baleanu, Dumitru; Ahmad, Shabir; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, Atangana-Baleanu fractional derivative has got much attention of the researchers due to its nonlocality and non-singularity. This operator contains an accurate kernel that describes the better dynamics of systems with a memory effect. In this paper, we investigate the fractional-order tumour-immune-vitamin model (TIVM) under Mittag-Leffler derivative. The existence of at least one solution and a unique solution has discussed through fixed point results. We established the Hyres-Ulam stability of the proposed model under the Mittag-Leffler derivative. The fractional Adams-Bashforth method has used to achieve numerical results. Finally, we simulate the obtained numerical results for different fractional orders to show the effect of vitamin intervention on decreased tumour cell growth and cancer risk. At the end of the paper, the conclusion has provided.
Citation - WoS: 11
Citation - Scopus: 13
Analytical Solutions for Free Convection Flow of Casson Nanofluid Over an Infinite Vertical Plate
(Amer inst Mathematical Sciences-aims, 2021) Asjad, Muhammad Imran; Akgul, Ali; Baleanu, Dumitru; Ahmad, Mushtaq; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This research article is design to elaborate the rule and significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluids namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermophysical properties of nanoparticles. Also the geometric and thermal conditions are imposed in flow domain. In the governing equations, the partial derivative with respect to time replaced by new hybrid fractional derivative and then solved analytically for temperature and velocity field with the help of Laplace transformed. The obtained solutions for temperature and velocity are presented geometrically by Mathcad software to see the effectiveness of potent parameters. The temperature and velocity present a significant increasing trend for increasing volume fraction parameter. The obtained results for temperature as well as velocity are also compared with the existing literature and it is concluded that field variables with new hybrid fractional derivative, show more decaying trend as compare to the results with Caputo and Caputo-Fabrizio fractional derivatives.
Citation - WoS: 12
Citation - Scopus: 16
Approximate Solutions To the Conformable Rosenau-Hyman Equation Using the Two-Step Adomian Decomposition Method With Pade Approximation
(Wiley, 2020) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Akgul, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper adopts the Adomian decomposition method and the Pade approximation techniques to derive the approximate solutions of a conformable Rosenau-Hyman equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing both the analytic and approximate solutions.
Citation - WoS: 1
Comparison on Solving a Class of Nonlinear Systems of Partial Differential Equations and Multiple Solutions of Second Order Differential Equations
(Springer international Publishing Ag, 2019) Akgul, Esra Karatas; Khan, Yasir; Baleanu, Dumitru; Akgul, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 3
Citation - Scopus: 3
Computational Analysis of Covid-19 Model Outbreak With Singular and Nonlocal Operator
(Amer inst Mathematical Sciences-aims, 2022) Farman, Muhammad; Akgul, Ali; Partohaghighi, Mohammad; Jarad, Fahd; Amin, Maryam; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of R0 and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.
Citation - WoS: 17
Citation - Scopus: 18
Construction and Numerical Analysis of a Fuzzy Non-Standard Computational Method for the Solution of an Seiqr Model of Covid-19 Dynamics
(Amer inst Mathematical Sciences-aims, 2022) Ahmed, Nauman; Rafiq, Muhammad; Akgul, Ali; Raza, Ali; Ahmad, Muhammad Ozair; Jarad, Fahd; Dayan, Fazal; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.
Citation - WoS: 27
Citation - Scopus: 31
Dynamical Transmission of Coronavirus Model With Analysis and Simulation
(Tech Science Press, 2021) Baleanu, Dumitru; Akgul, Ali; Ahmad, Aqeel; Saleem, Muhammad Umer; Farman, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
COVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R-0 is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.
Citation - WoS: 72
Citation - Scopus: 70
Dynamics Exploration for a Fractional-Order Delayed Zooplankton-Phytoplankton System
(Pergamon-elsevier Science Ltd, 2023) Gao, Rong; Xu, Changjin; Li, Ying; Akgul, Ali; Baleanu, Dumitru; Li, Peiluan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, we are concerned with the dynamics of a new established fractional-order delayed zooplankton- phytoplankton system. The existence and uniqueness of the solution are proved via Banach fixed point theorem. Non-negativeness of the solution is studied by mathematical inequality technique. The boundedness of the solution is analyzed by virtue of constructing an appropriate function. A novel delay-independent sufficient condition ensuring the stability and the onset of Hopf bifurcation for the established fractional -order delayed zooplankton-phytoplankton system is derived by means of Laplace transform, stability criterion and bifurcation knowledge of fractional-order differential equation. The global stability condition for the involved fractional-order delayed zooplankton-phytoplankton system is built by using a suitable positive definite function. Taking advantage of hybrid control tactics, we effectively control the time of occurrence of Hopf bifurcation for the established fractional-order delayed zooplankton-phytoplankton system. The study manifests that delay plays a vital role in controlling the stability and the time of occurrence of Hopf bifurcation for the involved fractional-order delayed zooplankton-phytoplankton system and the fractional -order controlled zooplankton-phytoplankton system involving delays. To verify the correctness of established chief results, computer simulation figures are distinctly displayed. The derived conclusions of this research are entirely new and possess potential theoretical value in preserving the balance of biological population. Up to now, there are few publications on detailed and comprehensive dynamic analysis on fractional-order delayed zooplankton-phytoplankton system via various exploration ways.
Citation - WoS: 27
Citation - Scopus: 29
Dynamics of Hiv-Tb Coinfection Model Using Classical and Caputo Piecewise Operator: a Dynamic Approach With Real Data From South-East Asia, European and American Regions
(Pergamon-elsevier Science Ltd, 2022) Liu, Zixin; Pang, Yicheng; Akgul, Ali; Baleanu, Dumitru; Xu, Changjin; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, we analyse the behaviour of the coinfection of the HIV-TB model using a piecewise operator in the classical-Caputo sense. For the aforementioned disease model, we present the existence as well as the uniqueness of a solution having a piecewise derivative. We also study the different versions of stability using Ulam-Hyers stability in nonlinear analysis. We use the piecewise Newton polynomial technique to obtain an approximation of the solution to the proposed problem. The simulations for the suggested coinfection model are presented. The simulations are carried out for the disease-free as well as endemic equilibrium. Additionally, the comparison between the simulated and real data is presented, where we obtain the best-fitted dynamics of the infected class with TB.
Citation - WoS: 79
Citation - Scopus: 86
Effects of Hybrid Nanofluid on Novel Fractional Model of Heat Transfer Flow Between Two Parallel Plates
(Elsevier, 2021) Asjad, Muhammad Imran; Akgul, Ali; Baleanu, Dumitru; Ikram, Muhammad Danish; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, it has been discussed the fractional model of Brinkman type fluid (BTF) holding hybrid nanoparticles. Titanium dioxide (TiO2) and silver (Ag) nanoparticles were liquefied in water (H2O) (base fluid) to make a hybrid nanofluid. The magnetohydrodynamic (MHD) free convection flow of the nanofluid (Ag - TiO2 - H2O)was measured in a bounded microchannel. The BTF model was generalized using constant proportional Caputo fractional operator (CPC) with effective thermophysical properties. By introducing dimensionless variables, the governing equations of the model were solved by Laplace transform method. The testified outcomes are stated as M-function. The impact of associated parameters were measured graphically using Mathcad and offered a comparison with the existing results from the literature. The effect of related parameters was physically discussed. It was concluded that constant proportional Caputo fractional operator (CPC) showed better memory effect than Caputo-Fabrizio fractional operator (CF) (Saqib et al., 2020). (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 41
Citation - Scopus: 45
Effects of Non-Linear Thermal Radiation and Chemical Reaction on Time Dependent Flow of Williamson Nanofluid With Combine Electrical Mhd and Activation Energy
(Shahid Chamran Univ Ahvaz, Iran, 2021) Waqas, Hassan; Asjad, M., I; Akgul, Ali; Baleanu, Dumitru; Danish, Gulzar Ahmad; Imran, M.; Tahir, Madeeha; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The current article will present the impact of the heat and mass transfer of combine electrical MHD flow of time dependent Williamson fluid with nanoparticles by the incorporating the influences of non-linear thermal radiation and the chemical reaction through wedge shape geometry. The fluid flows past a porous stretching wedge with convected Nield boundary conditions. The several (geometrical and physical) conditions have been included to provide more practicable results. The effects of activation energy further discussed. Due to relevant similarity transformation, set of partial differential equations which is non-linear and complicated is converted into simplest system of ordinary differential equations. To obtain the desired solution, famous numerical technique (shooting) used with the help of bvp4c MATLAB coding. The variation physical quantities namely velocity, temperature, concentration of nanoparticles, local Sherwood number, coefficient of skin friction and local Nusselt number have been observed under the influence of emerging parameters. The elaborated discussion presented with graphical and tabular illustrations.
Citation - WoS: 22
Citation - Scopus: 25
Epidemiological Analysis of the Coronavirus Disease Outbreak With Random Effects
(Tech Science Press, 2021) Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Naeem, Muhammad; Baleanu, Dumitru; Farman, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Today, coronavirus appears as a serious challenge to the whole world. Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis. New data on COVID-19 are available daily, yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited, and uncertainty remains around nearly all its parameters' values. This research provides the scientific and public health communities better resources, knowledge, and tools to improve their ability to control the infectious diseases. Using the publicly available data on the ongoing pandemic, the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections. Formulation of the testing hypotheses for different countries with a 95% level of confidence, and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries. The results will be helpful in decision making as well as in further mathematical analysis and control strategy. Statistical tools are used to investigate this pandemic, which will be useful for further research. The testing of the hypothesis is done for the differences in various effects including standard errors. Changes in states' variables are observed over time. The rapid outbreak of coronavirus can be stopped by reducing its transmission. Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.
Citation - WoS: 1
Citation - Scopus: 1
Finite Difference Method for Transmission Dynamics of Contagious Bovine Pleuropneumonia
(Amer inst Mathematical Sciences-aims, 2022) Modanli, Mahmut; Akgul, Ali; Jarad, Fahd; Kikpinar, Sait; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by finite difference method are presented. This model is made up of sensitive, exposed, vaccinated, infectious, constantly infected, and treated compartments. The model is studied by the finite difference method. Firstly, the finite difference scheme is constructed. Then the stability estimates are proved for this model. As a result, several simulations are given for this model on the verge of antibiotic therapy. From these figures, the supposition that 50% of infectious cattle take antibiotic therapy or the date of infection decrease to 28 days, 50% of susceptible obtain vaccination within 73 days.
Citation - WoS: 22
Citation - Scopus: 28
A Finite Difference Scheme To Solve a Fractional Order Epidemic Model of Computer Virus
(Amer inst Mathematical Sciences-aims, 2023) Iqbal, Zafar; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Jarad, Fahd; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.
Citation - WoS: 18
Citation - Scopus: 19
Fractional Order Mathematical Model of Serial Killing With Different Choices of Control Strategy
(Mdpi, 2022) Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd; Rahman, Mati Ur; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.