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Öğe 2-Absorbing Vague Weakly Complete ?-Ideals in ?-Rings(Mdpi, 2023) Onar, Serkan; Hila, Kostaq; Etemad, Sina; Akgül, Ali; De la sen, Manuel; Rezapour, ShahramThe aim of this study is to provide a generalization of prime vague Gamma-ideals in Gamma-rings by introducing non-symmetric 2-absorbing vague weakly complete Gamma-ideals of commutative Gamma-rings. A novel algebraic structure of a primary vague Gamma-ideal of a commutative Gamma-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Gamma-ideals of Gamma-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Gamma-ideals and 2-absorbing Gamma-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Gamma-ideal of a Gamma-ring and 2-absorbing K-vague Gamma-ideal of a Gamma-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Gamma-ring of R induced by a 2-absorbing vague weakly complete Gamma-ideal of a 2-absorbing Gamma-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Gamma-ideal.Öğe A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis(2023) Ahmed, Idris; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, KamsingIn recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model's complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters.Öğe A comparison on solutions of fifth-order boundary-value problems(Natural Sciences Publishing USA, 2016) Akgül, Ali; Inc, Mustafa; Kiliçman, AdemA 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.Öğe A Novel Method for Solving Nonlinear Jerk Equations(Springer Science and Business Media Deutschland GmbH, 2021) Akgül, Ali; Akgül, Esra KaratasIn this article, reproducing kernel method for solving Jerk equations is given. Convergence of the solution is shown. This method is applied to the equation for chosen values of the parameters that seem in the model and some numerical experiments prove that the reproducing kernel method is very effective method. © 2020, Springer Nature Switzerland AG.Öğe A novel method for the solution of blasius equation in semi-infinite domains(2017) Akgül, AliIn this work, we apply the reproducing kernel method for investigating Blasiusequations with two different boundary conditions in semi-infinite domains.Convergence analysis of the reproducing kernel method is given. The numericalapproximations are presented and compared with some other techniques,Keywords: Howarth’s numerical solution and Runge-Kutta Fehlberg method.Öğe A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives.(Public Library of Science, 2024) Khan, Zareen A; Riaz, Muhammad Bilal; Liaqat, Muhammad Imran; Akgül, AliFractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions. For this reason, methods for approximating solutions that occasionally yield closed-form solutions are crucial for solving these equations. This study introduces a novel technique that combines the residual function and a modified fractional power series with the Elzaki transform to solve various nonlinear problems within the Caputo derivative framework. The accuracy and effectiveness of our approach are validated through analyses of absolute, relative, and residual errors. We utilize the limit principle at zero to identify the coefficients of the series solution terms, while other methods, including variational iteration, homotopy perturbation, and Adomian, depend on integration. In contrast, the residual power series method uses differentiation, and both approaches encounter difficulties in fractional contexts. Furthermore, the effectiveness of our approach in addressing nonlinear problems without relying on Adomian and He polynomials enhances its superiority over various approximate series solution techniques.Öğe A Quantitative Approach to nth -Order Nonlinear Fuzzy Integro-Differential Equation(Springer, 2022) Ul Haq, Mansoor; Ullah, Aman; Ahmad, Shabir; Akgül, AliIn recent decades, both the fuzzy differential and fuzzy integral equations have attracted the researcher because the fuzzy operators produce appropriate predictions of problems in an uncertain environment. In this paper, we use fuzzy concepts to study nth-order nonlinear integro-differential equations. For the proposed problem, through the modified fuzzy Laplace transform method, we derive the general procedure of the solution. To demonstrate the accuracy and appropriateness of the method, we present some numerical problems. We also provide graphical representation by the use of Matlab 2017 to compare the exact and approximate solution. We solve different problems having second-order, fifth-order, and a system of nonlinear fuzzy integro-differential equations through the developed scheme. We simulate the numerical results via 2D and 3D graphs for the different values of uncertainty. In the end, we provide the discussion and concluding remarks of the article. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.Öğe A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect(Elsevier B.V., 2023) Ahmad, Bilal; Ozair Ahmad, Muhammad; Farman, Muhammad; Akgül, Ali; Riaz, Muhammad BilalThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations are nonlinear, the partial differential equations are transformed into ordinary differential equations using a workable similarity transformation. By using the Bvp4c module of the MATLAB program, the simplified mathematical framework can be numerically solved. The computation of Coefficients of skin friction, Nusselt numbers, different patterns of velocity profiles, fluid temperature, and concentration profiles reveals the physical nature of this study. As compared to earlier investigations, it was found that the obtained results demonstrated high degrees of symmetry and precision. A decline observes in velocity for boosted values of MHD, inclination, and rotatory parameter. However thermal transportation increases by increasing brownien motion, thermophoresis, radiation and Sorrot effect. The study has significant application in heat control systems, food factories, thermal exchangers, biomechanics, biomedical engineering, and aero dynamical systems © 2022Öğe ANALYSIS AND DYNAMICS OF CHOLERA EPIDEMIC SYSTEM IN SOCIETY VIA FRACTAL-FRACTIONAL OPERATOR(2025-01-01) Abbas, Fakhar; Ghaffar, Abdul; Akgül, Ali; Ahmad, Aqeel; Mustafa, Ghulam; Hendy A.S.; Abdallah, Suhad Ali Osman; El-Gawaad, N.S. AbdTo comprehend the dynamics of disease propagation within a society, mathematical formulation is a crucial tool to understand the complex dynamics. In order to transform the mathematical model with the objective of bolstering the immune system into a fractional-order model, we use the definition of Fractal-Fractional with Mittag-Leffler kernel. For an assessment of the stable position of a recently modified system, qualitative as well as quantitative assessments are carried out. We validate the property positivity and reliability of the developed system by evaluating its boundedness and uniqueness, which are important features of an epidemic model. The positive solutions with linear growth have been verified by the global derivative, and the level of effects of different parameters in each sub-section is determined through employing Lipschitz criteria. By employing Lyapunov’s first and second derivatives of the function, the framework is examined on a global scale to evaluate the overall effect with symptomatic and asymptomatic measures. Bifurcation analysis was performed to check the behavior of each sub-compartment under different parameters effects. The Mittag-Leffler kernel is used to obtain a robust solution via Fractal-Fractional operator for continuous monitoring of spread and control of cholera disease under different dimensions. Simulations are carried out to observe both the symptomatic and asymptomatic consequences of cholera globally, also to observe the actual behavior of cholera disease for control measures, and it has been confirmed that those with strong immune systems individuals recover early due to early detection measures. The actual state of cholera disease can be controlled by taking the following measures: early detection of disease for both individuals receiving medication and those who do not require medication because of their robust immune systems. This kind of research will be beneficial in determining how diseases spread and in developing effective control plans based on our validated findings.Öğe Analysis and simulation of fractional-order diabetes model(Erdal Karapinar, 2020) Ahmad, Aqeel; Farman, Muhammad; Akgül, AliIn this article, we research the diabetes model and its consequences using the Caputo and Atangana Baleanu fractional derivatives. A deterministic mathematical model is corresponding to the fractional derivative of diabetes mellitus. The Laplace transformation is used for the diagnostic structure of the diabetes model. Picard-Lindelof 's method shows the existence and uniqueness of the solution. Finally, numerical simulations are made to illustrate the effects of changing the fractional-order to obtain the theoretical results, and comparisons are made for the Caputo and Atangana Baleanu derivative. The results of the following work by controlling plasma glucose with the fractional-order model make it a suitable candidate for controlling human type 1 diabetes. © 2020, Erdal Karapinar. All rights reserved.Öğe Analysis of e-cigarette smoking model by a novel technique(Elsevier, 2022) Akgül, Ali; Akgül, Esra KaratasIn this chapter, we research an e-cigarette smoking model with the fractal-fractional derivatives. We use three different (power-law, exponential-decay, and Mittag-Leffler) kernels in the model. We apply a novel technique to the model. We obtain the numerical simulations to show the accuracy of the proposed method. © 2022 Elsevier Inc. All rights reserved.Öğe Analysis of Fractional Order Computer VirusModel with MultipleWays of Infections Potential(L and H Scientific Publishing, LLC, 2023) Akgül, Ali; Farman, Muhammad; Akram, Muhammad Mannan; Sajjad, Assad; Azeem, MuhammadIn this paper, we propose a novel technique for the computer virus epidemic which contains infected external computer effects and removable storage media on the computer viruses. The positivity and boundedness for validation of the model are also discussed. The existence and uniqueness of the system of solutions for the model are made by using fixed point theory and iterative method. Numerical simulation obtained with proposed scheme which shows the impacts of varying the fraction-al-order parameters and the support of the theoretical results. © 2023 L&H Scientific Publishing, LLC. All rights reserved.Öğe Analysis of Nonlinear Mathematical Model of COVID-19 via Fractional-Order Piecewise Derivative(Akif AKGUL, 2023) Sinan, Muhammad; Shah, Kamal; Abdeljawad, Thabet; Akgül, AliShort memory and long memory terms are excellently explained using the concept of piecewise fractional order derivatives. In this research work, we investigate dynamical systems addressing COVID-19 under piecewise equations with fractional order derivative (FOD). Here, we study the sensitivity of the proposed model by using some tools from the nonlinear analysis. Additionally, we develop a numerical scheme to simulate the model against various fractional orders by using Matlab 2016. All the results are presented graphically. © 2023 Chaos Theory and Applications. All rights reserved.Öğe Analysis of the Fractal-Fractional Modelling of Immune-Tumor Problem(Springer, 2022) Partohaghighi, Mohammad; Rubasinghe, Kalani; Akgül, Ali; Akgül, Esra KaratasCancer is one of the biggest threats around the globe, albeit medical action has been prosperous, despite large challenges, at least for some diagnostics. A magnificent effort of personal and financial resources is dedicated, with flourishing results(but also with failures), to cancer analysis with special consideration to experimental and analytical immunology. Fractal-fractional operators have manifested the enigmatic performance of numerous natural phenoms, which ordinarily do not foretell in ordinary ones and fractional operators. In this study, we examine an Immune-Tumor dynamical system supporting the fractal-fractional frame. We authenticate the existence theory to guarantee the suggested system maintains at least one answer through Schauder’s fixed point theorem. Additionally, Banach’s fixed theory affirms the uniqueness of the answer to the aimed problem. A Non-linear functional examination was carried out to affirm that the introduced system is stable with respect to Ulam-Hyres’s theory supporting the fractal-fractional operator. Behavior of the offered problem is presented through the graphical representations, for the different amounts of fractional order and fractal orders successfully. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.Öğe Analysis of Time Fractional Diffusion Equation Arising in Ocean Pollution with Different Kernels(Springer, 2023) Ullah, Inayat; Ullah, Aman; Ahmad, Shabir; Ikramullah; Akgül, AliThe objective of this paper is to look the solution of the ocean oil equations under the three different fractional operators. We analyze the fractional ocean oil equation in one dimension using the Caputo fractional derivative. Then, using the Caputo–Fabrizio derivative, we investigate the same ocean oil equation. Finally, the Atangana–Baleanu derivative is applied to the same problem. In comparison to other analytical approaches, the Laplace transform (LT) is an easy and efficient method which has a good convergence rate for the precise solution. As a result, we employ the LT to achieve the suggested equation’s series solution. To explore the efficiency and validity of the suggested method, we present two examples of the provided equation. The error analysis of is carried out through computationally and graphically. The comparison between different Caputo, CF and ABC ocean oil equation is provided through numeric data and graphs. Finally, we offer a conclusion as well as a physical explanation of the figures. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.Öğe Analytical investigation of space–time shifted nonlocal stochastic Sasa–Satsuma equation using the enhanced modified extended tanh-expansion method for stochastic solitary waves Solutions(Elsevier B.V., 2024) Manzoor, Zuha; Ashraf, Farrah; Iqbal, Muhammad Sajid; Akgül, Ali; Misro, Md YushalifyIn this paper, discover exact solutions of the space–time shifted nonlocal stochastic Sasa–Satsuma equations using the enhanced modified extended tanh-expansion method. This method is a sophisticated mathematical approach for analytical and approximate solution of a nonlinear partial differential equations. The space–time shifted nonlocal stochastic Sasa–Satsuma equations define the behavior of two complex-valued functions, u and v, in a nonlinear system. These equations are complicated to solve analytically because they contain a number of components that describe space–time shifting, nonlocal interactions, and stochastic problems. To increase reliability and effectiveness of the solutions, this method couples the extended tanh-function method with an enhanced method. In order to demonstrate how white noise affects the solutions to the space–time shifted nonlocal stochastic Sasa–Satsuma equations, we also use Matlab to create 3D surfaces and contour graphs of exact solutions. © 2024 The Author(s)Öğe Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm(Elsevier B.V., 2021) Jhangeer, Adil; Faridi, Waqas Ali; Asjad, Muhammad Imran; Akgül, AliThis paper aims to study an improved perturbed Schrödinger equation (IPSE) with a kind of Kerr law non-linearity equation governing the propagation dynamics of soliton in optical fibers through the nano-optical fiber. The considered model predicts the influence of quantic non-linearity on the motion of ultrashort optical pulses. The integrability of the model is accompanied by the transformed rational function V-expansion method (for simplicity [Formula presented]). This proposed method is a significant mathematical tool to obtain the exact travelings wave solutions of non-linear complex partial differential equations (PDEs). A bunch of soliton solutions like dark, dark singular, plane wave solution, and periodic are retrieved along with suitable parametric values. The graphical analysis is also presented for the description of propagation of waves expressed by rational functions, hyperbolic functions, and trigonometric functions. © 2021 The Author(s)Öğe Application of fractional derivative on non-linear biochemical reaction models(KeAi Communications Co., 2020) Akgül, Ali; Khoshnaw, SarbazH.A.Systems of ordinary differential equations play an important role in analyzing the dynamics for real world situations such as cell signaling pathways, population growth, enzymatic inhibitor reactions, and ecological models. Although, using differential equations have a great advantage to understand the dynamical behavior for such systems but most of the biological models have memory or sometimes called after effects. Such effects in the systems are often neglected. The idea of fractional-order differential equations gives a great role in understanding and identifying these effects on the model dynamics. In this paper, we review the basic ideas of fractional differential equations and their applications on non-linear biochemical reaction models. We apply this idea to a non-linear model of enzyme inhibitor reactions. The suggested method provides a good step forwards to understand the model dynamics in complex enzymatic reactions. We use a numerical approach to calculate some computational simulation of the model for different initial conditions and parameters. © 2020 The Author(s)Öğe Approximate Solutions for Higher Order Linear and Nonlinear Boundary Value Problems(Springer, 2021) Habib, Siddra; Azam, Muhammad Khurshid; Asjad, Muhammad Imran; Akgül, AliPurpose: The specific objective of this study is to examine the higher order nonlinear BVPs (12th and 13th orders) which perform efficient role in the modeling of physical problems of science and engineering. Design/methodology/approach: An innovative modification of the homotopy perturbation (HP) technique by coupling it with the Laplace transform (LT) has been expended to solve linear and nonlinear higher order boundary-value problems (BVPs). A homotopy is constructed for the given problems (BVPs) by HP technique and solved it by temporal Laplace method. Then Laplace inversion procedure has been used for retrieving the initial dominion solution. Motivation: The motivation of this paper is to introduce an improved and fast converging technique to solve complex higher order nonlinear boundary value problems. Findings: The main finding in this paper is to analyze the higher order nonlinear ordinary differential equations with more accurate approximate solutions. The proposed HPLT solutions show that the present technique provides more accurate, efficient, fast convergence and comparatively small absolute errors for extensive finite range. The authors found no assumption for the constriction of this approach. The computer software Maple has been used to compute numerical results of BVPs. The results obtained from HPLT method are found in excellent agreement with the exact solutions. Research limitations/implications: This paper invokes these two main inspirations: firstly, Laplace transform is associated with homotopy perturbation method in a new manner, secondly, handling of boundary value problems with higher order. Practical implications: In this paper, the values of the approximate solution have excellent Promise with those of exact solutions. Social implications: This paper presents a valuable technique for handling the nonlinear higher order differential equations (ODEs) without involving any restrictions or hypothesis. Originality: The work in present article is original and advanced. Significantly, no such work has yet been published in the literature. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.Öğe Attribution of Multi-slips and Bioconvection for Micropolar Nanofluids Transpiration Through Porous Medium over an Extending Sheet with PST and PHF Conditions(Springer, 2021) Abdal, Sohaib; Habib, Usama; Siddique, Imran; Akgül, Ali; Ali, BaghIn order to cope with the rising thermal imbalances in important technological activities, efficient heat transfer attracts the attention of this work. An exploration for the multi-slip effects pertaining to micropolar-based nanofluid transportation through a porous medium in the presence of two thermal boundaries prescribed surface temperature and prescribed heat flux. The material and energy transportation takes place over an extending sheet. Arrhenius activation energy and thermal radiation are considered whereas a magnetic field of uniform strength acts normally to the sheet. Bio-convection is peculiar phenomena to avoid the possible settling of nano-entities. Moreover, the impact for three cases of mass transpiration (injection fw> 0 , impermeable wall fw= 0 , suction fw< 0) are taken into account. The fundamental formulation has developed a system of partial differential equations. With the help of similarity transformation, the leading equations are transmuted into ordinary differential equations. The fourth-order Runge–Kutta method with shooting techniques is employed to attain the numerical solutions. The impacts of physical parameters are displayed with the help of tables and graphs for two cases of thermal boundaries. The buoyancy ratio parameters Nr and bio convection Raleigh number decelerate the flow. The parameter of thermophoresis and Brownian motion enhances the temperature. Cattaneo–Christov parameter and Prandtl number reduce the temperature. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
