Sürdürülebilir Kalkınma Amaçları
Yayınlar
- MakaleAçık Erişim2026A New Caputo-Fabrizio Hybrid Method for the Numerical Solution of Caputo-Fabrizio Fractional Epidemic Model
Anaç, Halil; Alkan, Asli
This paper presents a novel Caputo–Fabrizio hybrid numerical method for examining the dynamics of fractional epidemic models defined by memory effects and non-singular kernels. The proposed method combines the Caputo–Fabrizio fractional derivative with a hybrid transform framework, facilitating the derivation of accurate and convergent approximate solutions for nonlinear epidemic systems. The model's parameters are analyzed in relation to infection transmission and recovery dynamics, whereas the fractional order α regulates the magnitude of memory and genetic influences. Numerical simulations indicate that the novel hybrid method exhibits remarkable concordance with established results for integer-order scenarios, while showcasing enhanced precision, computing efficiency, and robustness in fractional contexts. The suggested method offers a versatile and effective analytical instrument for investigating real-world epidemic occurrences exhibiting long-term memory traits.
- MakaleAçık Erişim2026Semianalytical Solutions of a Caputo-Fabrizio Fractional Epidemic Model via the q-Kushare Homotopy Transform Method
Alkan, Asli; Anaç, Halil
In this study, an enhanced semianalytical framework is developed for solving nonlinear fractional differential equations involving the Caputo-Fabrizio fractional operator. The proposed Caputo-Fabrizio q-Kushare homotopy analysis transform method (CFq-KHATM) combines the Caputo-Fabrizio derivative, Kushare transform, and q-homotopy analysis within a unified operator-consistent framework. Unlike conventional hybrid approaches, the method preserves the nonsingular exponential memory structure of the Caputo-Fabrizio derivative and provides additional convergence-control flexibility through the auxiliary parameter & hbar; and q-deformation parameter n. To demonstrate its applicability, a Caputo-Fabrizio fractional epidemic model with memory-dependent transmission dynamics is investigated. Numerical simulations for different fractional-order values show that memory effects significantly influence epidemic evolution, infection persistence, and environmental viral dynamics. Furthermore, comparisons with existing methods together with absolute and relative error analyses confirm the accuracy, stability, and convergence efficiency of the proposed framework. The obtained results indicate that CFq-KHATM is a flexible and computationally reliable tool for nonlinear fractional epidemic systems and other memory-dependent dynamical models.
- BildiriAçık Erişim2026The New Numerical Solutions of the Atangana-Baleanu Fractional Benney Equation
Alkan, Aslı; Anaç, Halil; Duman, O.; Erkus-Duman, E.
This study focuses on the novel Atangana-Baleanu method employed to obtain new numerical solutions for the Benney equation with Atangana-Baleanu fractional derivatives. The Atangana-Baleanu q-Elzaki homotopy analysis transform method is used to numerically solve this equation. This paper presents an investigation of the numerical solutions obtained using this technique. Furthermore, the proposed method has been subjected to numerical simulation using Maple software, considering different fractional orders.
- MakaleAçık Erişim2026The novel conformable methods to solve conformable time- fractional coupled Whitham-Broer-Kaup equation
Alkan, Aslı; Avit, Özkan; Anaç, Halil
This study employs two innovative techniques, namely the conformable q-homotopy analysis transform method (Cq-HATM) and the conformable Elzaki Adomian decomposition method (CEADM), to investigate the numerical solutions for the conformable time-fractional coupled Whitham-Broer-Kaup problem. One of the two novel approaches offered is Cq-HATM, which is a hybrid approach that integrates the q-homotopy analysis transform method with Laplace transform using the concept of conformable derivative. The CEADM method, like the aforementioned approach, is a hybrid method that integrates the Adomian decomposition method and Elzaki transform by utilizing the concept of conformable derivative. The computer simulations were conducted in order to provide empirical evidence supporting the efficacy and reliability of the recommended methodologies. Upon comparing the precise solutions with the obtained solutions, it becomes evident that both of the novel methodologies exhibit simplicity, efficacy, and proficiency in addressing nonlinear conformable time-fractional partial differential equations.
- Kitap BölümüYalnız künye2025The Robust Method for Solving the Conformable Time-Fractional Klein–Gordon Equation
Anaç, Halil
The present study used the conformable fractional q-Shehu homotopy analysis transform method to investigate the conformable time-fractional Klein–Gordon equations with proportional delay. The numerical answers to this problem are graphed using Maple software. The efficacy and consistency of the proposed method have been demonstrated through numerical simulations.
- MakaleAçık Erişim2025The analysis of Caputo-Fabrizio fractional plastic waste model with a new numerical method; [Caputo-Fabrizio kesirli mertebeden plastik atık modelinin yeni bir sayısal yöntemle analizi]
Bingöl, Sait; Anaç, Halil
In this paper, the new numerical solutions for Caputo-Fabrizio fractional plastic waste model are derived utilizing a novel hybrid approach known as the Caputo-Fabrizio fractional q-formable homotopy analysis transform method. A novel hybrid method combining the Caputo-Fabrizio transform and the q-homotopy analysis method is introduced. A plastic waste model generally denotes a conceptual or mathematical framework employed to comprehend, simulate, or forecast the movement, accumulation, and effects of plastic trash within a system, spanning from local surroundings to the global scale. The plastic waste model is analyzed in the Caputo-Fabrizio fractional framework. The solutions for the Caputo-Fabrizio fractional plastic waste model are illustrated in the Maple program.
- MakaleAçık Erişim2024The Efficient Robust Conformable Methods for Solving the Conformable Fractional Cahn-Allen Equation
Anaç, Halil; Avit, Özkan
This study focuses on the novel conformable methods employed to obtain new numerical solutions for the Cahn-Allen equation with conformable fractional derivatives. One of the two distinct methods put forth is the Cq-HATM, a hybrid technique that integrates the q-homotopy analysis transform method with the Laplace transform, utilizing the definition of conformable derivative. The CHPETM is a hybrid technique that combines the homotopy perturbation method with the Elzaki transform (ET). New numerical solutions of the conformal fractional differential Cahn-Allen equation were obtained using CHPETM and Cq-HATM. The computer simulations have been conducted in order to provide validation for the efficacy and reliability of the proposed methods. Upon performing a comparative analysis between the exact solutions and the solutions obtained through the novel methods, it becomes evident that both of these approaches exhibit simplicity, efficacy, and proficiency in addressing nonlinear conformable time-fractional coupled systems.
- MakaleAçık Erişim2024The novel conformable methods to solve conformable time- fractional coupled jaulent-miodek system
Anaç, Halil; Avit, Özkan
This research utilizes two novel methods, specifically the conformable q-homotopy analysis transform method (Cq-HATM) and the conformable Elzaki Adomian decomposition method (CEADM), to examine the numerical solutions for the conformable time-fractional coupled Jaulent-Miodek system. One of the two unique methods proposed is the Cq-HATM, which is a hybrid approach that combines the q-homotopy analysis transform method with the Laplace transform, employing the concept of conformable derivative. The CEADM method, similar to the aforementioned approach, is a hybrid technique that combines the Adomian decomposition method with Elzaki transform through the utilization of the concept of conformable derivative. The computer simulations were performed to offer validation for the effectiveness and dependability of the suggested approaches. After conducting a comparison between the exact solutions and the solutions acquired using the unique methods, it is apparent that both of these approaches demonstrate simplicity, effectiveness, and competency in tackling nonlinear conformable time-fractional coupled systems.
- MakaleAçık Erişim2024A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative
Alkan, Aslı; Anaç, Halil
In this research, we propose a new numerical method that combines with the Caputo-Fabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the Caputo-Fabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results.
- MakaleAçık Erişim2024A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation
Bektaş, Umut; Anaç, Halil
This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table.
- MakaleAçık Erişim2024The novel numerical solutions for time-fractional Fornberg-Whitham equation by using fractional natural transform decomposition method
Alkan, Aslı; Anaç, Halil
The time-fractional partial differential equations were solved by the fractional natural transform decomposition method. Fractional derivatives are Caputo sense. The Fornberg-Whitham equation is a generalization of the Korteweg-de Vries (KdV) equation, which describes the propagation of long waves in shallow water. It includes higher-order dispersion terms, making it applicable to a wider range of dispersive media the fractional natural transform decomposition method (FNTDM) was also used to examine applications, and the solutions obtained by this method have been compared to those obtained by the variational iteration method, fractional variational iteration method, and homotopy perturbation method. In addition, the MAPLE package drew graphs of the solutions of nonlinear time-fractional partial differential equations, taking into account physics. The method described in this study exhibited a notable degree of computational precision and straightforwardness when used to the analysis and resolution of intricate phenomena pertaining to fractional nonlinear partial differential equations within the domains of science and technology.
- MakaleAçık Erişim2023Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods
Olgun, Ali; Anaç, Halil; Kartal, Abdullah
By using two new methods, called the conformable fractional q-homotopy analysis transform method and the conformable Shehu homotopy perturbation method, the conformable time-fractional partial differential equations with proportional delay is analysed. The graphs of this equation's numerical solutions are drawn. According to numerical simulations, the proposed methods are effective and reliable.
- MakaleAçık Erişim2023Q-homotopy shehu analysis transform method of time-fractional coupled burgers equations
Anaç, Halil; Bektaş, Umut
In this study, numerical solutions to time-fractional coupled Burgers equations are obtained utilizing the q-homotopy Shehu analysis transform method. The definition of fractional derivatives in the sense of Caputo. q-homotopy Shehu analysis transform method is also used to find the numerical solutions of the time-fractional coupled Burgers equations. In addition, the MAPLE software is utilized to plot the graphs of the solutions. These results demonstrate that the presented method is accurate and simple to implement.
- MakaleYalnız künye2023The New Conformable Methods to Solve Conformable Time- Fractional Generalized Burgers Equation with Proportional Delay
Anaç, Halil; Avcı, Halil Hüseyin
In this article, two novel methods called conformable q-Mohand homotopy analysis transform method (Cq-MHATM) and conformable Mohand Adomian decomposition method (CMADM) are utilized to examine the novel numerical solutions for nonlinear conformable time-fractional generalized Burgers equation with proportional delay. The first of the two new methods suggested, Cq- MHATM, is a hybrid method that combines q-homotopy analysis transform method and Mohand transform in the sense of comformable derivative. The other method, CMADM is also a hybrid method that combines Adomian decomposition method and Mohand transform in the sense of comformable derivative. The computer simulations were worked out to prove that the suggested methods work and are trusted.
- MakaleAçık Erişim2023The Numerical Solutions of the Conformable Time-Fractional Noyes Field Model via a New Hybrid Method
Öner, Bedir Kaan; Anaç, Halil
This article employs a novel method, namely the conformable q-Sawi homotopy analysis transform method (Cq-SHATM) to investigate the numerical solutions of the nonlinear conformable time-fractional Noyes-Field model. The proposed method, namely Cq-SHATM, is a hybrid approach that integrates the q-homotopy analysis transform method and the Sawi transform using the concept of conformable derivative. 3D graps of the solutions obtained with this method were drawn. Additionally, 2D graphs of the solutions were obtained in the Maple software program. The computer simulations were conducted in order to validate the efficacy and reliability of the proposed method.
- MakaleAçık Erişim2023The new numerical solutions of conformable time fractional generalized Burgers equation with proportional delay; [Oransal gecikmeli uyumlu zaman kesirli mertebeden genelleştirilmiş Burgers denkleminin yeni sayısal çözümleri]
Kartal, Abdullah; Anaç, Halil; Olgun, Ali
The conformable time-fractional partial differential equations with proportional delay are studied using two new methods: the conformable fractional q-homotopy analysis transform method and the conformable Shehu homotopy perturbation method. The numerical solutions to this equation are graphed. Numerical simulations show that the proposed techniques are effective and trustworthy.
- MakaleAçık Erişim2022Homotopi pertürbasyon Elzaki dönüşümü yöntemi ile doğrusal olmayan zaman-kesirli kısmi diferansiyel denklemler için yeni yaklaşık analitik çözümler
Anaç, Halil
Bazı doğrusal olmayan zaman-kesirli mertebeden kısmi diferansiyel denklemler, homotopi pertürbasyon Elzaki dönüşümü yöntemi ile çözülmüştür. Kesirli türevler Caputo anlamında tanımlanmıştır. Uygulamalar homotopi pertürbasyon Elzaki dönüşümü yöntemi ile incelenmiştir. Bunun yanında, çözümlerin grafikleri MAPLE yazılımında çizdirilmiştir. Ayrıca homotopi pertürbasyon Elzaki dönüşümü yöntemi ve homotopi pertürbasyon Sumudu dönüşümü yöntemi çözümlerinin, lineer olmayan zaman- kesirli mertebeden kısmi diferansiyel denklemlerin tam çözümü ile mutlak hata karşılaştırması sunulmaktadır. Ek olarak, bu mutlak hata karşılaştırması tablolarda belirtilmiştir. Bu makalenin yeniliği, hem Caputo kesir dereceli gaz dinamiği denkleminin hem de Caputo kesir dereceli Klein-Gordon denkleminin bu yöntemle ilk analizidir. Bu nedenle, homotopi pertürbasyon Elzaki dönüşümü yöntemi, zaman-kesirli mertebeden kısmi diferansiyel denklemlerin analitik çözümlerinin elde edilmesinde hızlı ve etkilidir.
- MakaleAçık Erişim2022Conformable Fractional Elzaki Decomposition Method of Conformable Fractional Space-Time Fractional Telegraph Equations
Anaç, Halil
Conformable space-time fractional linear telegraph equations are examined using a new method known as conformable fractional Elzaki decomposition method. The suggested method combines the Adomian decomposition method with the conformable fractional Elzaki transform. It is found that numerical simulations confirm the effectiveness and reliability of the proposed method.
- MakaleYalnız künye2020APPLICATION OF CRANK-NICOLSON METHOD TO A RANDOM COMPONENT HEAT EQUATION
Anaç, Halil; Merdan, Mehmet; Kesemen, Tülay
In this study, the solution of a random component heat equation is obtained by using Crank-Nicolson Method. The initial condition of this equation is examined by Normal distribution. The expected value and variance of solution of this equation are obtained. Crank-Nicolson method is applied to analyze the solution of this equation. Also, the solution and the graphs of the expected value and variance are obtained by using MATLAB software. The results of the heat equation are compared with random characteristics of this equation. Firstly, a random component heat equation is solved by this method.
- MakaleAçık Erişim2020Solving for the random component time-fractional partial differential equations with the new Sumudu transform iterative method
Anaç, Halil; Merdan, Mehmet; Kesemen, Tülay
The new Sumudu transform iterative method is implemented to get the approximate solutions of random component time-fractional partial differential equations with Caputo derivative. The parameters and the initial conditions of the random component time-fractional partial differential equations are analyzed with Gamma distribution. The expected values and variances of these solutions are calculated, and the graphs of the expected values and variances are plotted in Maple software. The results for the random component time-fractional partial differential equations with Gamma distribution are examined to investigate effects of this distribution on results. The numerical experiments indicate that this method is very effective.