Yazar "Inc, Mustafa" seçeneğine göre listele

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    A comparison on solutions of fifth-order boundary-value problems
    (Natural Sciences Publishing USA, 2016) Akgül, Ali; Inc, Mustafa; Kiliçman, Adem
    A fast and accurate numerical scheme for the solution of fifth-order boundary-value problems has been investigated in this work. We apply the reproducing kernel method (RKM) for solving this problem. The analytical results of the equations have been acquired in terms of convergent series with easily computable components. We compare our results with the numerical methods: B-spline method, decomposition method, variational iteration method, Sinc-Galerkin method and homotopy perturbation method. The comparison of the results with exact ones is made to confirm the validity and efficiency. © 2016 NSP.
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    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, Dumitru
    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.
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    A new approach for one-dimensional sine-Gordon equation
    (Springer International Publishing Ag, 2016) Akgul, Ali; Inc, Mustafa; Kilicman, Adem; Baleanu, Dumitru
    In this work, we use a reproducing kernel method for investigating the sine-Gordon equation with initial and boundary conditions. Numerical experiments are studied to show the efficiency of the technique. The acquired results are compared with the exact solutions and results obtained by different methods. These results indicate that the reproducing kernel method is very effective.
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    A Study of Nanofluid Flow with Free Bio-Convection in 3D Nearby Stagnation Point by Hermite Wavelet Technique
    (Amer Scientific Publishers, 2024) Raghunatha, K. R.; Kumbinarasaiah, S.; Inc, Mustafa; Akgul, Ali
    A new wavelet-numerical method for solving a system of partial differential equations describing an incompressible bio-convection nanofluid flow in a three-dimensional region close to the stagnation point is the primary focus of this article. Hermite wavelets form the basis of the algorithm. An assortment of similitude factors is utilized to improve on the overseeing conditions addressing the protection of all out mass, force, nuclear power, nanoparticles, and microorganisms to a bunch of completely connected nonlinear common differential conditions. The most important physical quantities that have a practical impact on the spread of motile bacteria are presented and analyzed in this paper. During bio-convection, the Prandtl, Lewis, Peclet, Schmidt, and Rayleigh numbers can alter the distribution of moving molecules. The dispersion of microorganisms can be emphatically affected by the kinds of nanoparticles and by the varietis in the temperature as well as volumetric part of the IP: 203.8.109.20 On: Tue, 16 Apr 2024 14:56:17 nanoparticles between the wall and the encompassing liquid. With excellent agreement for coupled nonlinear differential equations in engineering applications, our result demonstrates how powerful and simple the HWM Delivered by Ingenta is for solving these coupled nonlinear ordinary differential equations.
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    An exact solution of heat and mass transfer analysis on hydrodynamic magneto nanofluid over an infinite inclined plate using Caputo fractional derivative model
    (Amer Inst Mathematical Sciences-Aims, 2022) Kayalvizhi, J.; Kumar, A. G. Vijaya; Sene, Ndolane; Akguel, Ali; Inc, Mustafa; Abu-Zinadah, Hanaa; Abdel-Khalek, S.
    This paper presents the problem modeled using Caputo fractional derivatives with an accurate study of the MHD unsteady flow of Nanofluid through an inclined plate with the mass diffusion effect in association with the energy equation. H2O is thought to be a base liquid with clay nanoparticles floating in it in a uniform way. Bousinessq's approach is used in the momentum equation for pressure gradient. The nondimensional fluid temperature, species concentration, and fluid transport are derived together with Jacob Fourier sine and Laplace transforms Techniques in terms of exponential decay function, whose inverse is computed further in terms of Mittag-Leffler function. The impact of various physical quantities interpreted with fractional order of the Caputo derivatives. The obtained temperature, transport, and species concentration profiles show behaviours for 0 < alpha <1 where alpha is the fractional parameter. Numerical calculations have been carried out for the rate of heat transmission and the Sherwood number is swotted to be put in the form of tables. The parameters for the magnetic field and the angle of inclination slow down the boundary layer of momentum. The distributions of velocity, temperature, and concentration expand more rapidly for higher values of the fractional parameter. Additionally, it is revealed that for the volume fraction of nanofluids, the concentration profiles behave in the opposite manner. The limiting case solutions also presented on flow field of governing model.
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    An investigation of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system: Lie symmetry reductions, invariant solutions, dynamical behaviors and conservation laws
    (Elsevier, 2022) Kumar, Sachin; Kumar, Amit; Inc, Mustafa; Alotaibi, Hammad; Abdou, M. A.; Akguel, Ali
    In this study, we develop the asymmetric Nizhnik-Novikov-Veselov (ANNV) system in (2+1)-dimensions, which has applications in processes of interaction of exponentially localized wave structures, as well as the infinitesimal generators, Lie symmetries, vector fields, and the commutator table. The link between Lie symmetry vectors and conserved vectors is constructed using symmetry conservation principles once Lie point symmetries are first deduced. Using the aforementioned Lie symmetry technique, two-stage symmetry reductions are used to obtain the precise analytical answers. These analytical solutions all incorporate a number of different functional parameters as well as arbitrary constant parameters. The diversity of the physical phenomena of the obtained soliton solutions is illustrated by the inclusion of arbitraryness of functional parameters and constants. By using Noether's method, conservation laws have subsequently been attained. The innovative aspect of the work described in this paper is an attempt to use 3-dimensional and 2-dimensional visuals, along with appropriate arbitrary parameter selections and functional parameter values, to represent the dynamical behavior of the solutions that have been produced. In order to make this research more intriguing, stripe solitons, dark-bright solitons, solitary waves, singular wave-form soliton, and other types of soliton wave profiles of the achieved solutions are described. The effectiveness, benefits, and utility of the employed approach are demonstrated by the physical and graphical interpretation of the answers attained.
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    ANALYSIS OF FRACTIONAL ORDER DIARRHEA MODEL USING FRACTAL FRACTIONAL OPERATOR
    (World Scientific Publ Co Pte Ltd, 2022) Yao, Shao-Wen; Ahniad, Aqui; Inc, Mustafa; Farman, Muhammad; Ghaffar, Abdul; Akgul, Ali
    In this paper, we construct a scheme of fractional-order mathematical model for the population infected by diarrhea disease by using the four compartments S, I, T and R. The fractal-fractional derivative operator (FFO) with generalized Mittag-Leffler kernel is employed to obtain the solution of the proposed system. The system is analyzed qualitatively as well as verify non-negative unique solution. The existence and uniqueness results of fractional-order model under Atangana-Baleanu fractal-fractional operator have been proved by fixed point theory. Also error analysis has been made for the proposed fractional-order model. Simulation has been carried out for derived fractional-order scheme to check the effectiveness of the results which will help, how to prevent and control such type of epidemic in society.
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    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, Mustafa
    This 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.
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    Analytical treatment of the couple stress fluid-filled thin elastic tubes
    (Elsevier Gmbh, Urban & Fischer Verlag, 2017) Hashemi, Mir Sajjad; Inc, Mustafa; Akgul, Ali
    In this paper, we present the symmetries and self-adjointness of the problem about the couple stress fluid-filled thin elastic tubes. Some soliton solutions of the specified problem are constructed with the aid of Lie group symmetry method. (C) 2017 Elsevier GmbH. All rights reserved.
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    Application of Extended Adomian Decomposition Method and Extended Variational Iteration Method to Hirota-Satsuma Coupled KdV Equation
    (Amer Scientific Publishers, 2017) Inc, Mustafa; Gencoglu, M. Tuncay; Akgul, Ali
    We acquire series solutions of Hirota-Satsuma coupled KdV (HSCKdV) equation with initial condition by using extended adomian decomposition method (EADM) and extended variational iteration method (EVIM). We compare these solutions with the some solutions that are exist in the literature. Obtained tables and figures show that EADM and EVIM give more accurate results than some methods in the literature. Furthermore, approximate solution that obtained by the convergence parameter of these methods is closer to the exact solution for big and small values of the time.
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    Approximate solutions to the conformable Rosenau-Hyman equation using the two-step Adomian decomposition method with Pade approximation
    (Wiley, 2020) Akgul, Ali; Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru
    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.
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    Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain
    (Amer Inst Mathematical Sciences-Aims, 2023) Muhammad, Noor; Asghar, Ali; Irum, Samina; Akgul, Ali; Khalil, E. M.; Inc, Mustafa
    In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition (C) in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.
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    Classifications of Soliton Solutions of the Generalized Benjamin-Bona-Mahony Equation with Power-Law Nonlinearity
    (Amer Scientific Publishers, 2018) Inc, Mustafa; Akgul, Ali
    In this work, the order reduction technique and He's variational principle are used for exact solutions of the nonlinearly dispersive generalized Benjamin-Bona-Mahony (shortly BBM(m,n)) equation with power-law nonlinearity. Therefore, we acquire compactons, solitary patterns, solitary wave and periodic wave solutions for this equation. We illustrate that the analytical methods are very efficient to present the physical behaviors of the solutions of nonlinear evolution equations. Additionally, the constraint conditions for the existence of these solutions are presented.
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    Dynamical behavior of cancer cell densities in two dimensional domain by the representation theory of solitons
    (Elsevier, 2023) Iqbal, Muhammad Sajid; Ahmed, Nauman; Naeem, Rishi; Akgul, Ali; Razzaque, Abdul; Inc, Mustafa; Khurshid, Hina
    This article analyzes the mathematical model which is described by the nonlinear partial differential equation governing the density of cancer cells at any position (x, y) in the open bounded subset of the plane at any time t. This is a two-dimensional model that describes the dynamics of cancer cells under radiotherapy and its comparison with the one in the absence of radiation effects. The 06-model expansion method has been used to find the exact solutions of the underlying problem. The simulation of obtained results have also been argued.(c) 2023 Elsevier B.V. All rights reserved.
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    Exact special solutions of space-time fractional Cahn-Allen equation by beta and M-truncated derivatives
    (World Scientific Publ Co Pte Ltd, 2024) Sadaf, Maasoomah; Akram, Ghazala; Inc, Mustafa; Dawood, Mirfa; Rezazadeh, Hadi; Akgul, Ali
    In this paper, we consider the nonlinear space-time fractional form of Cahn-Allen equation (FCAE) with beta and M-truncated derivatives. Cahn-Allen equation (CAE) is commonly used in many problems of physics and engineering, such as, solidification problems, phase separation in iron alloys and others. We apply the improved tan(?(?)2)-expansion method (ITEM). We obtain four types of traveling wave solutions, including, trigonometric, hyperbolic, rational and exponential function solutions. We demonstrate some of the extracted solutions using definitions of the beta (BD) and M-truncated derivatives (MTD) to understand their dynamical behavior. We observe the fractional effects of the aforementioned derivatives on the related physical phenomena up to possible extent.
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    Fractional order COVID-19 model with transmission rout infected through environment
    (Amer Inst Mathematical Sciences-Aims, 2022) Yao, Shao-Wen; Farman, Muhammad; Amin, Maryam; Inc, Mustafa; Akgul, Ali; Ahmad, Aqeel
    In this paper, we study a fractional order COVID-19 model using different techniques and analysis. The sumudu transform is applied with the environment as a route of infection in society to the proposed fractional-order model. It plays a significant part in issues of medical and engineering as well as its analysis in community. Initially, we present the model formation and its sensitivity analysis. Further, the uniqueness and stability analysis has been made for COVID-19 also used the iterative scheme with fixed point theorem. After using the Adams-Moulton rule to support our results, we examine some results using the fractal fractional operator. Demonstrate the numerical simulations to prove the efficiency of the given techniques. We illustrate the visual depiction of sensitive parameters that reveal the decrease and triumph over the virus within the network. We can reduce the virus by the appropriate recognition of the individuals in community of Saudi Arabia.
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    Fractional study of a novel hyper-chaotic model involving single non-linearity
    (Elsevier, 2022) Partohaghighi, Mohammad; Veeresha, P.; Akguel, Ali; Inc, Mustafa; Riaz, Muhamamad Bilal
    The applications of hyperchaotic systems (HCSs) can be widely seen in diverse fields associated with engineering due to their complicated dynamics, randomness, and high delicacy and sensibility. In the present work, we aim to investigate a new hyper-chaotic system involving a single non-linearity under the fractional Caputo-Fabrizio (CF) derivative for the first time. In fact, there is no previous study using fractional derivatives in this system. A new mathematical system using a fractional-order operator will be designed with the novel operator. The Caputo-Fabrizio non-integer operator is aimed to be employed to capture complex nature. In order to solve the extracted dynamical system, a quadratic numerical scheme is applied. This study contains stability and convergence sections for the considered method. Moreover, numerical results of the problem under various values of fractional orders and different values of initial conditions (ICs) are provided to show the performance of the suggested scheme. Figures of solutions for each dependent variable can be observed.
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    Group preserving scheme and reproducing kernel method for the Poisson-Boltzmann equation for semiconductor devices
    (Springer, 2017) Akgul, Ali; Inc, Mustafa; Hashemi, Mir Sajjad
    This paper introduces that the nonlinear Poisson-Boltzmann equation for semiconductor devices describing potential distribution in a double-gate metal oxide semiconductor field effect transistor (DG-MOSFET) is exactly solvable. The DG-MOSFET shows one of the most advanced device structures in semiconductor technology and is a primary focus of modeling efforts in the semiconductor industry. Lie symmetry properties of this model is investigated in order to extract some exact solutions. The reproducing kernel Hilbert space method and group preserving scheme also have been applied to the nonlinear equation. Numerical results show that the present methods are very effective.
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    Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model
    (Elsevier, 2021) Hussain, Ghulam; Khan, Tahir; Khan, Amir; Inc, Mustafa; Zaman, Gul; Nisar, Kottakkaran Sooppy; Akgul, Ali
    Novel coronavirus disease is a burning issue all over the world. Spreading of the novel coronavirus having the characteristic of rapid transmission whenever the air molecules or the freely existed virus includes in the surrounding and therefore the spread of virus follows a stochastic process instead of deterministic. We assume a stochastic model to investigate the transmission dynamics of the novel coronavirus. To do this, we formulate the model according to the charectersitics of the corona virus disease and then prove the existence as well as the uniqueness of the global positive solution to show the well posed-ness and feasibility of the problem. Following the theory of dynamical systems as well as by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions of the extinction and the existence of stationary distribution. Finally, we carry out the large scale numerical simulations to demonstrate the verification of our analytical results. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
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    New approach for the Fornberg-Whitham type equations
    (Elsevier Science Bv, 2017) Boutarfa, Bariza; Akgul, Ali; Inc, Mustafa
    This paper applies the reproducing kernel Hilbert space method to the solutions of three types of Fornberg-Whitham equations: original, modified and time fractional. Comparison with Adomian decomposition method, homotopy analysis method and the variational iteration method shows the validity and applicability of the technique. (C) 2015 Elsevier B.V. All rights reserved.