Yazar "Abbasbandy, Saeid" seçeneğine göre listele

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    A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations
    (IOP publishing Ltd, 2024) Amoozad, Taher; Abbasbandy, Saeid; Sahihi, Hussein; Allahviranloo, Tofigh
    In this article, a new implementation of the reproducing kernel method is presented for solving systems of fractional-order Volterra integro-differential equations. Unlike previous implementations, this method does not rely on the Gram-Schmidt process. The reproducing kernel method utilizes various components, including space, inner product, bases, and points. Furthermore, the system of fractional-order Volterra integro-differential equations involves Caputo's fractional derivative and Volterra integral. However, when using the reproducing kernel method to solve these systems, challenges such as longer execution time and lower accuracy may arise compared to other methods. The present method has overcome these challenges with features such as easy implementation, high accuracy, and lower execution time.
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    A new application of the reproducing kernel method for solving linear systems of fractional order Volterra integro-differential equations
    (Institute of Physics, 2024) Amoozad, Taher; Abbasbandy, Saeid; Sahihi, Hussein; Allahviranloo, Tofigh
    In this article, a new implementation of the reproducing kernel method is presented for solving systems of fractional-order Volterra integro-differential equations. Unlike previous implementations, this method does not rely on the Gram-Schmidt process. The reproducing kernel method utilizes various components, including space, inner product, bases, and points. Furthermore, the system of fractional-order Volterra integro-differential equations involves Caputo’s fractional derivative and Volterra integral. However, when using the reproducing kernel method to solve these systems, challenges such as longer execution time and lower accuracy may arise compared to other methods. The present method has overcome these challenges with features such as easy implementation, high accuracy, and lower execution time. © 2024 IOP Publishing Ltd.
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    Application of the reproducing kernel method for solving linear Volterra integral equations with variable coefficients
    (Iop Publishing Ltd, 2024) Amoozad, Taher; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.
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    Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems
    (Springernature, 2024) Rasekhinezhad, Hajar; Abbasbandy, Saeid; Allahviranloo, Tofigh; Baboliand, Esmail
    This paper studies the variable fractional functional boundary value problems (VFF-BVPs) by considering Caputo fractional derivative. We use the reproducing kernel method (RKM) without the orthogonalization process as a smart scheme. For this purpose, we construct a reproducing kernel that does not satisfy the boundary condition of VFF-BVP. With this kernel, we can better approximate the solutions for VFF-BVP. Using this method increases the accuracy of the approximate solution so that a significant error analysis can be produced. Finally, two numerical examples are solved to illustrate the efficiency of the present method.
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    Generalized Hukuhara conformable fractional derivative and its application to fuzzy fractional partial differential equations
    (SPRINGER, 2022) Ghaffari, Manizheh; Allahviranloo, Tofigh; Abbasbandy, Saeid; Azhini, Mahdi
    The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. To achieve this, the fuzzy conformable fractional derivative based on the generalized Hukuhara differentiability is defined, and several properties are brought on the topic, such as switching points and the fuzzy chain rule. After that, a new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional wave equation and the fuzzy fractional diffusion equation. The present work is the first report in which the fuzzy traveling wave method is used to design an analytical method to solve these fuzzy problems. The final examples are asserted that our new method is applicable and efficient.
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    Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter
    (Springer nature, 2025) Najafi, Seyed Esmaeil Sadat; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This paper introduces an innovative approach that marries the spectral method with a time-dependent partial differential equation filter to tackle the phenomenon of shock waves in traffic flow modeling. Through the strategic application of Discrete low-pass filters, this method effectively mitigates shock-induced deviations, leading to significantly more accurate results compared to conventional spectral techniques. We conduct a thorough examination of the stability conditions inherent to this approach, providing valuable insights into its robustness. To substantiate its effectiveness, we present a series of numerical examples illustrating the method's prowess in delivering precise solutions. Comparative analysis against established methods such as Lax and Cu reveals a marked superiority in accuracy. This work not only contributes a novel numerical technique to the field of traffic flow modeling but also addresses a persistent challenge, offering a promising avenue for further research and practical applications.
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    Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter
    (Springer nature, 2025) Najafi, Seyed Esmaeil Sadat; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This paper introduces an innovative approach that marries the spectral method with a time-dependent partial differential equation filter to tackle the phenomenon of shock waves in traffic flow modeling. Through the strategic application of Discrete low-pass filters, this method effectively mitigates shock-induced deviations, leading to significantly more accurate results compared to conventional spectral techniques. We conduct a thorough examination of the stability conditions inherent to this approach, providing valuable insights into its robustness. To substantiate its effectiveness, we present a series of numerical examples illustrating the method's prowess in delivering precise solutions. Comparative analysis against established methods such as Lax and Cu reveals a marked superiority in accuracy. This work not only contributes a novel numerical technique to the field of traffic flow modeling but also addresses a persistent challenge, offering a promising avenue for further research and practical applications.
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    On the properties and applications of fuzzy analytic equations
    (Elsevier B.V., 2021) Sabzi, Kh; Allahviranloo, Tofigh; Abbasbandy, Saeid
    This paper presents the fuzzy power series method to solve the second-order differential equation under generalized Hukuhara differentiability with fuzzy and real coefficients. For this purpose, different types of fuzzy analytic functions by attention to generalized Hukuhara differentiability, ordinary and singular points are introduced. Since in the discussion of fuzzy power series, the concept of the fuzzy convergence radius is one of the most essential and fundamental concepts, the fuzzy convergence radius under the generalized division is defined. Fundamental theorems, such as fuzzy ratio tests, the convergence of the fuzzy geometric series, are expressed and proven. In addition, it has been shown that the fuzzy convergence radius of fuzzy power series does not change concerning derivatives under operators such as derivatives and integrals. It has been shown that the fuzzy analytic functions are still fuzzy analytic functions concerning derivatives under fuzzy operators, summation, multiplication, and generalized division. Then, the uniqueness of the solution of the second-order fuzzy differential equations with fuzzy and real coefficients in the form of a fuzzy power series by attention to the type of generalized differentiability is shown. Finally, there are examples to demonstrate the effectiveness of the method.
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    Solving a System of Linear Equations Based on Z-Numbers to Determinate the Market Balance Value
    (Hindawi Ltd, 2023) Pour, Zeinab Motamedi; Allahviranloo, Tofigh; Kermani, Mozhdeh Afshar; Abbasbandy, Saeid
    In this article, a general linear equations system with Z-number's data is introduced. Since the nature of Z-numbers has two parameters, namely, reliability and fuzziness, it is difficult to find the exact solution to these systems. Therefore, a numerical procedure for calculating the solution is designed. The proposed method is illustrated with some applied examples. Determining the value of the market balance is one of the examined examples.
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    Two-dimensional muntz-legendre wavelet method for fuzzy hybrid differential equations
    (World Scientific, 2022) Shahryari, N.; Allahviranloo, T.; Abbasbandy, Saeid
    In this paper, the fuzzy approximate solutions for the fuzzy Hybrid differential equation emphasizing the type of generalized Hukuhara differentiability of the solutions are obtained by using the two-dimensional Muntz-Legendre wavelet method. To do this, the fuzzy Hybrid differential equation is transformed into a system of linear algebraic equations in a matrix form. Thus, by solving this system, the unknown coefficients are obtained. The convergence of the proposed method is established in detail. Numerical results reveal that the two-dimensional Muntz-Legendre wavelet is very effective and convenient for solving the fuzzy Hybrid differential equation. © 2023 World Scientific Publishing Company.
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    Using a new implementation of reproducing kernel Hilbert space method to solve a system of second-order BVPs
    (Springernature, 2023) Amoozad, Taher; Allahviranloo, Tofigh; Abbasbandy, Saeid; Rostamy Malkhalifeh, Mohsen
    In this paper, a new implementation based on the reproducing kernel method (RKM) without the Gram-Schmidt orthogonalization for solving linear and nonlinear systems of second-order boundary value problems is presented. In the RKM method, components such as points, space, inner product, bases, and a suitable method have an effect on increasing the accuracy. The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The compatibility of numerical results and theorems demonstrates that the Present method is effective.