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• MakaleAçık Erişim2026/r/gumushane/19374
  A 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.

  İncele
• MakaleAçık Erişim2026/r/gumushane/16198
  Semianalytical 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.

  İncele
• BildiriAçık Erişim2026/r/gumushane/13805
  The New Numerical Solutions of the Atangana-Baleanu Fractional Benney Equation

  Alkan, Aslı; Anaç, Halil

  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.

  İncele
• MakaleAçık Erişim2026/r/gumushane/13609
  The 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.

  İncele
• Kitap BölümüYalnız künye2025/r/gumushane/14319
  The 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.

  İncele
• MakaleAçık Erişim2025/r/gumushane/12316
  The 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.

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  İncele
• MakaleAçık Erişim2024/r/gumushane/19890
  The 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.

  İncele
• MakaleAçık Erişim2024/r/gumushane/19836
  The 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.

  İncele
• MakaleAçık Erişim2024/r/gumushane/14428
  A 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.

  İncele
• MakaleAçık Erişim2024/r/gumushane/14235
  A 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.

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