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Your search keyword '"Irandoust-Pakchin, Safar"' showing total 4 results
Start Over Author "Irandoust-Pakchin, Safar" Topic fractional differential equations
4 results on '"Irandoust-Pakchin, Safar"'

1. A new approach of B-spline wavelets to solve fractional differential equations.

Author

Elahi, Abdollah, Irandoust-pakchin, Safar, Rahimi, Asghar, and Abdi-mazraeh, Somaiyeh

Subjects
*SPLINE theory, *PARTIAL differential equations, *ALGEBRAIC equations, *FRACTIONAL differential equations, *ORDINARY differential equations, *WAVELET transforms, *PROBLEM solving, *PSEUDOPOTENTIAL method
Abstract

This paper presents a groundbreaking method for solving the multi-order fractional differential (M-OFD), both linear and nonlinear, as well as fractional partial differential equations (FPDE)s. This approach involves constructing an operational matrix of fractional derivatives using linear B-spline (LB-S) wavelet functions with perfect subtlety. The new method has two crucial features. Firstly, it simplifies the problem by converting it into a set of algebraic equations, which is a significant advantage. This makes the method highly accurate and reliable. Secondly, it uses thresholding to dramatically reduce the computational workload in linear problems. This leads to lightning-fast and highly efficient problem-solving. The newly developed scheme underwent a thorough examination of its error estimates and convergence, revealing remarkable results in terms of accuracy and efficiency. The analysis provides a comprehensive understanding of the scheme's performance, highlighting its potential as a dependable and effective method. Based on the findings, it is evident that the proposed method not only delivers exceptional precision but also operates with remarkable efficiency. • The fractional differential equations are considered in the current work. • A numerical technique based on linear B-Spline wavelets is used to find its numerical solution. • Also the constructing the operational matrix of fractional derivative based of wavelets is main goal. • Thus the main problem is reduced to sparse problem of solving a system of algebraic equations. • The method is examined on several real and test examples of various types to show its efficiency. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Image deblurring using adaptive fractional‐order shock filter.

Author

Irandoust‐pakchin, Safar, Babapour, Shahab, and Lakestani, Mehrdad

Subjects
*IMAGE intensifiers, *MECHANICAL shock, *IMAGE reconstruction, *FRACTIONAL differential equations
Abstract

In this paper, a novel image enhancement model based on shock filter for image deblurring is proposed in three cases. For the weight of shock filter, the fractional‐order derivative of initial blurry image is used. This fractional‐order weight can be adjusted adaptively according to the gradient of blurred image. Compared with the traditional integer‐order shock filter, the proposed model creates less staircase effect, whereas the enhancement and deblurring of the resulted images are efficiently good. Stability properties of the proposed method are studied theoretically, and also to show the validity of stability studies results, some numerical experiments are presented. The three cases of proposed method are compared with together and with other methods. Different test images are used to show the validity of these cases. Numerical experiments confirm the efficiency of these cases. [ABSTRACT FROM AUTHOR]

Published
2021
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3. Numerical Solution for a Variable-Order Fractional Nonlinear Cable Equation via Chebyshev Cardinal Functions.

Author

Irandoust-Pakchin, Safar, Abdi-Mazraeh, Somayeh, and Khani, Ali

Subjects
*FRACTIONAL differential equations, *CHEBYSHEV series, *CAPUTO fractional derivatives, *BROWNIAN motion, *RIEMANN integral, *FRACTIONAL calculus
Abstract

In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique. [ABSTRACT FROM AUTHOR]

Published
2017
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4. Construction of new generating function based on linear barycentric rational interpolation for numerical solution of fractional differential equations.

Author

Irandoust-pakchin, Safar, Abdi-mazraeh, Somayeh, and Kheiri, Hossein

Subjects
*NUMERICAL solutions to differential equations, *GENERATING functions, *FRACTIONAL differential equations, *INTERPOLATION
Abstract

In this paper, a new generating function based on linear barycentric rational interpolation is introduced for the numerical solution of fractional differential equations which is designed on fractional linear multistep methods. The consistency of the proposed method is analyzed. considering monotonicity of the coefficients, the stability of the proposed method is presented. Also, the stability regions are determined which show the new scheme improves the stability properties and the accuracy compared with the fractional backward difference formulae. Finally, the extracted numerical results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Published
2020
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