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Öğe A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering(Amer Inst Physics, 2018) Khan, Yasir; Akgul, Ali; Faraz, Naeem; Inc, Mustafa; Akgul, Esra Karatas; Baleanu, DumitruIn 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.Öğe A New Application of the Sumudu Transform for the Falling Body Problem(Hindawi Ltd, 2021) Akgul, Esra Karatas; Akgul, Ali; Alqahtani, Rubayyi T.In this study, we investigate the falling body problem with three different fractional derivatives. We acquire the solutions of the model by the Sumudu transform. We show the accuracy of the Sumudu transform by some theoretic results and implementations.Öğe A novel method for analysing the fractal fractional integrator circuit(Elsevier, 2021) Akgul, Ali; Ahmad, Shabir; Ullah, Aman; Baleanu, Dumitru; Akgul, Esra KaratasIn this article, we propose the integrator circuit model by the fractal-fractional operator in which fractional-order has taken in the Atangana-Baleanu sense. Through Schauder's fixed point theorem, we establish existence theory to ensure that the model posses at least one solution and via Banach fixed theorem, we guarantee that the proposed model has a unique solution. We derive the results for Ulam-Hyres stability by mean of non-linear functional analysis which shows that the proposed model is Ulam-Hyres stable under the new fractal-fractional derivative. We establish the numerical results of the model under consideration through Atanaga-Toufik method. We simulate the numerical results for different sets of fractional order and fractal dimension.(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/).Öğe A Novel Method for Solutions of Fourth-Order Fractional Boundary Value Problems(Mdpi, 2019) Akgul, Ali; Akgul, Esra KaratasIn this paper, we find the solutions of fourth order fractional boundary value problems by using the reproducing kernel Hilbert space method. Firstly, the reproducing kernel Hilbert space method is introduced and then the method is applied to this kind problems. The experiments are discussed and the approximate solutions are obtained to be more correct compared to the other obtained results in the literature.Öğe A NOVEL METHOD FOR THE SPACE AND TIME FRACTIONAL BLOCH-TORREY EQUATIONS(Vinca Inst Nuclear Sci, 2018) Akgul, Esra KaratasReproducing kernel technique was implemented to solve the fractional Bloch-Torrey equations. This efficient technique was used via some useful reproducing kernel functions, to obtain approximations to the exact solution in form of series solutions. A numerical example has been presented to prove efficiency of developed technique.Öğe ANALYSIS OF HIDDEN ATTRACTORS OF NON-EQUILIBRIUM FRACTAL-FRACTIONAL CHAOTIC SYSTEM WITH ONE SIGNUM FUNCTION(World Scientific Publ Co Pte Ltd, 2022) Zhang, Lei; Ahmad, Shabir; Ullah, Aman; Akgul, Ali; Akgul, Esra KaratasIn 2017, Atangana proposed more generalized operators depending on two parameters: one is fractional order (FO) and other is fractal dimension. The novel operators are defined with three different kernels. These operators produced excellent dynamics of the chaotic systems. In this paper, the Caputo fractal-fractional operator is used to explore a chaotic system which contains only one signum function. The existence theory is developed by using the fixed-point result of Leray-Schauder to prove that the considered chaotic system possesses at least one solution. The proposed chaotic system has a unique solution, according to Banach's fixed-point theorem. We demonstrate that the suggested chaotic system is Ulam-Hyres (UH) stable under the novel operator of power law kernel by employing nonlinear functional analysis. The Adams-Bashforth technique is used to evaluate the numerical outcomes of the considered model. We show the complex structure of numerical solutions for different FO and fractal dimension values.Öğe Analysis of respiratory mechanics models with different kernels(De Gruyter Poland Sp Z O O, 2022) Akgul, Esra Karatas; Akgul, Ali; Jamshed, Wasim; Rehman, Zulfiqar; Nisar, Kottakkaran Sooppy; Alqahtani, Mohammed S.; Abbas, MohamedIn this article, we investigate the mechanics of breathing performed by a ventilator with different kernels by an effective integral transform. We mainly obtain the solutions of the fractional respiratory mechanics model. Our goal is to give the underlying model flexibly by making use of the advantages of the non-integer order operators. The big advantage of fractional derivatives is that we can formulate models describing much better the systems with memory effects. Fractional operators with different memories are related to different types of relaxation process of the non-local dynamical systems. Additionally, since we consider the utilisation of different kinds of fractional derivatives, most often having benefit in the implementation, the similarities and differences can be obviously seen between these derivatives.Öğe Analysis of the Fractional Differential Equations Using Two Different Methods(Mdpi, 2023) Partohaghighi, Mohammad; Akgul, Ali; Akgul, Esra Karatas; Attia, Nourhane; De la Sen, Manuel; Bayram, MustafaNumerical methods play an important role in modern mathematical research, especially studying the symmetry analysis and obtaining the numerical solutions of fractional differential equation. In the current work, we use two numerical schemes to deal with fractional differential equations. In the first case, a combination of the group preserving scheme and fictitious time integration method (FTIM) is considered to solve the problem. Firstly, we applied the FTIM role, and then the GPS came to integrate the obtained new system using initial conditions. Figure and tables containing the solutions are provided. The tabulated numerical simulations are compared with the reproducing kernel Hilbert space method (RKHSM) as well as the exact solution. The methodology of RKHSM mainly relies on the right choice of the reproducing kernel functions. The results confirm that the FTIM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed methods.Öğe ANALYTIC APPROXIMATE SOLUTIONS FOR FLUID-FLOW IN THE PRESENCE OF HEAT AND MASS TRANSFER(Vinca Inst Nuclear Sci, 2018) Kilicman, Adem; Khan, Yasir; Akgul, Ali; Faraz, Naeem; Akgul, Esra Karatas; Inc, MustafaThis paper outlines a comprehensive study of the fluid-flow in the presence of heat and mass transfer. The governing non-linear ODE are solved by means of the homotopy perturbation method. A comparison of the present solution is also made with the existing solution and excellent agreement is observed. The implementation of homotopy perturbation method proved to be extremely effective and highly suitable. The solution procedure explicitly elucidates the remarkable accuracy of the proposed algorithm.Öğe 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, Ali; Akgul, Esra Karatas; Khan, Yasir; Baleanu, Dumitru[Abstract Not Available]Öğe Computational examination of Jeffrey nanofluid through a stretchable surface employing Tiwari and Das model(De Gruyter Poland Sp Z O O, 2021) Shahzad, Faisal; Jamshed, Wasim; Koulali, Aimad; Aissa, Abederrahmane; Safdar, Rabia; Akgul, Esra Karatas; Ibrahim, Rabha W.In this research, we analyze the magnetohydrodynamics heat act of a viscous incompressible Jeffrey nanoliquid, which passed in the neighborhood of a linearly extending foil. As a process, we employ alumina (Al2O3) as nanoparticles, assuming that the base fluid is ethylene glycol. In this involvement, we consider the heating by Joule effect and viscous dissipation. We select the passable transformations, motion, and temperature formulas converting into non-linear differential equation arrangement. We solved the system by using a Keller-box method. Then, we provide a graphical description of outcomes according to the selected control parameters. Higher values of dissipation parameter cause a surge in temperature field as well as strengthen width of the heat boundary layer. The velocity, drag coefficient, and heat transfer (HT) rate for the base fluid are comparatively greater than that of the Al2O3-ethylene glycol nanofluid, although the temperature is embellished by the inclusion of nanoparticles. Moreover, we report depreciation in surface drag as well as HT by the virtue of amplification in the Deborah number. The proclaimed outcomes are advantageous to boost the incandescent light bulb's, cooling and heating processes, filament emitting light, energy generation, multiple heating devices, etc.Öğe COMPUTATIONAL SOLUTIONS OF FRACTIONAL ELECTRIC SYMMETRIC CIRCUITS BY SUMUDU TRANSFORMATION(World Scientific Publ Co Pte Ltd, 2023) Akgul, Esra Karatas; Jamshed, Wasim; Abdullaev, Sherzod Shukhratovich; Belgacem, Fethi Bin Muhammed; El Din, Sayed M.In this research, we study the Caputo fractional and constant proportional derivative numerical approximation of electrical symmetric circuits. It has been assumed that the derivative is in the order 0 <= sigma <= 1. For the fractional electrical symmetric circuits, the RC, LC, and RLC solutions are obtained by using the Sumudu transformation. We also compare the numerical simulation of each equation to its classical equivalent. We use a highly efficient integral transform to examine the impact of the power-law kernel. In our upcoming works, we will apply this to electrical circuits that are more intricate.Öğe Fractional modeling of COVID-19 pandemic model with real data from Pakistan under the ABC operator(Amer Inst Mathematical Sciences-Aims, 2022) Zarin, Rahat; Khan, Amir; Aurangzeb; Akgul, Ali; Akgul, Esra Karatas; Humphries, Usa WannasinghaIn this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.Öğe Frequency Analysis for Functionally Graded Material Cylindrical Shells: A Significant Case Study(Hindawi Ltd, 2021) Anwar, Rabia; Ghamkhar, Madiha; Khan, Muhammad Imran; Safdar, Rabia; Iqbal, Muhammad Zafar; Jamshed, Wasim; Akgul, Esra KaratasCylindrical shells play an important role for the construction of functionally graded materials (FGMs). Functionally graded materials are valuable in order to develop durable materials. They are made of two or more materials such as nickel, stainless steel, zirconia, and alumina. They are extremely beneficial for the manufacturing of structural elements. Functionally graded materials are broadly used in several fields such as chemistry, biomedicine, optics, and electronics. In the present research, vibrations of natural frequencies are investigated for different layered cylindrical shells, those constructed from FGMs. The behavior of shell vibration is based on different parameters of geometrical material. The problem of the shell is expressed from the constitutive relations of strain and stress with displacement, as well as it is adopted from Love's shell theory. Vibrations of natural frequencies (NFs) are calculated for simply supported-simply supported (SS-SS) and clamped-free (C-F) edge conditions. The Rayleigh-Ritz technique is employed to obtain the shell frequency equation. The shell equation is solved by MATLAB software.Öğe Impact of gold nanoparticles along with Maxwell velocity and Smoluchowski temperature slip boundary conditions on fluid flow: Sutterby model(Elsevier, 2022) Sajid, Tanveer; Jamshed, Wasim; Shahzad, Faisal; Akgul, Esra Karatas; Nisar, Kottakkaran Sooppy; Eid, Mohamed R.Communication is structured to develop a novel three dimensional mathematical model regarding rotating Sutterby fluid flow subjected to a slippery expandable sheet. The heat transfer analysis has been carried out with the inclusion of effects like gold nanoparticles and thermal radiation. The mass transfer regarding the concentration of the fluid has been analysed with the utilization of the activation energy effect. Maxwell velocity and Smoluchowksi temperature slip boundary conditions have been employed. The mathematically modelled partial differential equations (PDEs) regarding momentum, energy, and concentration step down into ordinary differential equations (ODEs) with the utilization of suitable transformation. Matlab built-in bvp4c numerical scheme has been used to handle dimensionless ODEs. The physical quantities like surface drag coefficient, heat transfer as well as mass transfer in the case of variation in various sundry parameters are numerically computed and displayed in the form of tables and figures. The temperature field amplifies by the virtue of augmentation in gold nanoparticles volume fraction and an increment in activation energy booms the mass fraction field. It is observed that the presence of the thermal radiation parameter enhances the heat transfer rate 17.2% and mass transfer booms 62.1% in the case reaction rate constant.Öğe Laplace Transform Method for Economic Models with Constant Proportional Caputo Derivative(Mdpi, 2020) Akgul, Esra Karatas; Akgul, Ali; Baleanu, DumitruIn 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.Öğe Mechanical improvement in solar aircraft by using tangent hyperbolic single-phase nanofluid(Sage Publications Ltd, 2021) Hussain, Syed M.; Jamshed, Wasim; Akgul, Esra Karatas; Nasir, Nor Ain Azeany MohdSolar power is the primary thermal energy source from the sunlight. This research has carried out the study of solar aircraft with solar radiation in enhancing efficiency. The thermal transfer inside the solar aircraft wings using a nanofluid past a parabolic surface trough collector (PTSC) is investigated thoroughly. The source of heat is regarded as solar radiation. For several impacts, such as porous medium, thermal radiation, and varying heat conductivity, the heat transmission performance of the wings is examined. By using the tangent hyperbolic nanofluid (THNF), the entropy analysis has been performed. The modeled momentum and energy equations are managed using the well-established numerical methodology known as the finite difference method. Two distinct kinds of nano solid-particles have been examined, such as Copper (Cu) and Zirconium dioxide (ZrO2), while Engine Oil (EO) being regarded as a based fluid. Different diagram parameters will be reviewed and revealed as figures and tables on speed, shear stress, temperature, and the surface drag coefficient and Nuselt number. It is observed that in terms of heat transfer for amplification of thermal radiation and changeable thermal conductance parameters, the performance of the aircraft wings raises. In contrast to traditional fluid, nanofluid is the best source of heat transmission. Cu-EO's thermal efficiency over ZrO2-EG falls to the minimum level of 12.6% and has reached a peak of 15.3%.Öğe New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives(Pergamon-Elsevier Science Ltd, 2021) Akgul, Esra Karatas; Akgul, Ali; Yavuz, MehmetWe investigate a couple of different financial/economic models based on market equilibrium and option pricing with three different fractional derivatives in this paper. We obtain the fundamental solutions of the models by Sumudu transform and Laplace transform. We demonstrate our results by illustrative figures to point out the difference between the fractional operators that have power kernel, exponential kernel and Mittag-Leffler kernel. We prove the efficiency and accuracy of the Sumudu transform and decomposition series method constructed by the Laplace transform in providing the solutions of several different linear/nonlinear financial models by considering the theoretical results and illustrative applications. It seems that the proposed method is an efficient way to solve such problems that contain different types of fractional operators and one is able to point out the differences between these mentioned operators. One of the valuable features of the method is the possibility of using it in solving other similar equations including fractional derivatives having a singular or nonsigular kernel. This paper also suggests a good initiative and profitable tool for those who want to invest in these types of options either individually or institutionally. (C) 2021 Elsevier Ltd. All rights reserved.Öğe New Numerical Method for Solving Tenth Order Boundary Value Problems(Mdpi, 2018) Akgul, Ali; Akgul, Esra Karatas; Baleanu, Dumitru; Inc, MustafaIn this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables.Öğe New numerical simulation of the oscillatory phenomena occurring in the bioethanol production process(Springer Heidelberg, 2023) Partohaghighi, Mohammad; Akgul, Ali; Akgul, Esra Karatas; Asad, Jihad; Safdar, Rabia; Yao, GuangmingThe process of bioethanol production has been characterized with a structured and nonsegregated form of yeast growth dynamics. In this work, a geometric numerical method is applied to obtain the approximate solution of the oscillatory phenomena transpiring in the process of bioethanol production. This method is called group preserving scheme which is based on Lie group, proper for solving ordinary differential equations. In this regard, The Minkowski Cayley transformation is used to create this numerical method to get the approximate solutions of the problems. Moreover, figures are provided to show the reliability and accuracy of the proposed method.
