Browsing by Author "Akgul, Ali"

Now showing 1 - 20 of 48

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
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: 48
Citation - Scopus: 57
Modelling and Analysis of a Measles Epidemic Model With the Constant Proportional Caputo Operator
(Mdpi, 2023) Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; De la Sen, Manuel; Farman, Muhammad
Despite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission of the disease with the influence of vaccination, we proposed a novel fractional order measles model with a constant proportional (CP) Caputo operator. We analysed the proposed model's positivity, boundedness, well-posedness, and biological viability. Reproductive and strength numbers were also verified to examine how the illness dynamically behaves in society. For local and global stability analysis, we introduced the Lyapunov function with first and second derivatives. In order to evaluate the fractional integral operator, we used different techniques to invert the PC and CPC operators. We also used our suggested model's fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis on the CPC and Hilfer generalised proportional operators. Employing the Laplace with the Adomian decomposition technique, we simulated a system of fractional differential equations numerically. Finally, numerical results and simulations were derived with the proposed measles model. The intricate and vital study of systems with symmetry is one of the many applications of contemporary fractional mathematical control. A strong tool that makes it possible to create numerical answers to a given fractional differential equation methodically is symmetry analysis. It is discovered that the proposed fractional order model provides a more realistic way of understanding the dynamics of a measles epidemic.
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
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: 2
Citation - Scopus: 4
A New Application of the Legendre Reproducing Kernel Method
(Amer inst Mathematical Sciences-aims, 2022) Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd; Foroutan, Mohammad Reza
In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.
Citation - WoS: 45
Citation - Scopus: 71
On Solutions of Fractional Riccati Differential Equations
(Springer international Publishing Ag, 2017) Akgul, Ali; Baleanu, Dumitru; Sakar, Mehmet Giyas
We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.
Citation - WoS: 43
Citation - Scopus: 44
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
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: 30
On Ψ-Hilfer Generalized Proportional Fractional Operators
(Amer inst Mathematical Sciences-aims, 2021) Ahmed, Idris; Akgul, Ali; Jarad, Fahd; Alha, Subhash; Mallah, Ishfaq
In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the psi-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.
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
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: 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
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: 44
Citation - Scopus: 50
Analysis of the Fractional Tumour-Immune Model With Mittag-Leffler Kernel
(Elsevier, 2020) Ullah, Aman; Akgul, Ali; Baleanu, Dumitru; Ahmad, Shabir
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: 1
Citation - Scopus: 1
Structure Preserving Numerical Analysis of Reaction-Diffusion Models
(Wiley, 2022) Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgul, Ali; Ahmed, Nauman
In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs.
Citation - WoS: 15
Citation - Scopus: 21
On the Solutions of Electrohydrodynamic Flow With Fractional Differential Equations by Reproducing Kernel Method
(de Gruyter Open Ltd, 2016) Baleanu, Dumitru; Inc, Mustafa; Tchier, Fairouz; Akgul, Ali
In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.
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
Citation - WoS: 24
Citation - Scopus: 29
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
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: 1
Citation - Scopus: 2
A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering
(Amer inst Physics, 2018) Akgul, Ali; Faraz, Naeem; Inc, Mustafa; Akgul, Esra Karatas; Baleanu, Dumitru; Khan, Yasir
In this paper, a highly nonlinear equations are treated analytically via homotopy perturbation method for fluid mechanics problem. The non-linear differential equations are transformed to a coupled non-linear ordinary, differential equations via similarity transformations. Graphical results are presented and discussed for various physical parameters.
Citation - WoS: 32
Citation - Scopus: 40
Laplace Transform Method for Economic Models With Constant Proportional Caputo Derivative
(Mdpi, 2020) Akgul, Ali; Baleanu, Dumitru; Akgul, Esra Karatas
In this study, we solved the economic models based on market equilibrium with constant proportional Caputo derivative using the Laplace transform. We proved the accuracy and efficiency of the method. We constructed the relations between the solutions of the problems and bivariate Mittag-Leffler functions.
Citation - WoS: 2
Solving the Nonlinear System of Third-Order Boundary Value Problems
(Springer international Publishing Ag, 2019) Akgul, Esra Karatas; Khan, Yasir; Baleanu, Dumitru; Akgul, Ali
Citation - WoS: 21
Citation - Scopus: 26
A Hybrid Analytical Technique for Solving Nonlinear Fractional Order Pdes of Power Law Kernel: Application To Kdv and Fornberg-Witham Equations
(Amer inst Mathematical Sciences-aims, 2022) Ullah, Aman; Akgul, Ali; Jarad, Fahd; Ahmad, Shabir
It is important to deal with the exact solution of nonlinear PDEs of non-integer orders. Integral transforms play a vital role in solving differential equations of integer and fractional orders. 'o obtain analytical solutions to integer and fractional-order DEs, a few transforms, such as Laplace transforms, Sumudu transforms, and Elzaki transforms, have been widely used by researchers. We propose the Yang transform homotopy perturbation (YTHP) technique in this paper. We present the relation of Yang transform (YT) with the Laplace transform. We find a formula for the YT of fractional derivative in Caputo sense. We deduce a procedure for computing the solution of fractional-order nonlinear PDEs involving the power-law kernel. We show the convergence and error estimate of the suggested method. We give some examples to illustrate the novel method. We provide a comparison between the approximate solution and exact solution through tables and graphs.
Citation - WoS: 23
Solutions of Nonlinear Systems by Reproducing Kernel Method
(int Scientific Research Publications, 2017) Khan, Yasir; Akgul, Esra Karatas; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Akgul, Ali
A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field. (C) 2017 All rights reserved.
Citation - WoS: 22
Citation - Scopus: 26
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
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.