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Approximate solution of Abel integral equation
Computers & Mathematics with Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Li, Huang, Yong, Li, Xian-Fang
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Partial, Composite Fractional Operators, and Their Properties and Applications
MATEC Web of Conferences, 2017 The paper discusses the properties of the partial fractional integrals, the partial fractional derivatives, and the composite fractional integrals and derivatives.
Deng Kaiying, Deng Jingwei, Li Suduo
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Electronic Journal of Qualitative Theory of Differential Equations, 2016 New and known properties of the resolvent of the kernel of linear Abel integral equations of the form \begin{equation} \tag{A$_\lambda$} x(t) = f(t) - \lambda \int_0^t (t - s)^{q-1}x(s)\,ds, \end{equation} where $\lambda > 0$ and $q \in (0,1)$, are ...
Leigh Becker
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Comparison of the Orthogonal Polynomial Solutions for Fractional Integral Equations
Mathematics, 2019 In this paper, a collocation method based on the orthogonal polynomials is presented to solve the fractional integral equations. Six numerical examples are given to illustrate the method. The results are compared with the other methods in the literature,
Ayşegül Daşcıoğlu, Serpil Salınan
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Dynamic Keynesian Model of Economic Growth with Memory and Lag
Mathematics, 2019 A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model.
Vasily E. Tarasov +1 more
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Abel's Integral Equation as a Convolution Transform [PDF]
Proceedings of the American Mathematical Society, 1956 the first equation to be treated and solved as an integral equation, has an extensive literature, dealing on the one hand with properties of the functions involved, and on the other hand with the solution, and conditions for solubility of the equation. In the first category one might cite, in the modern spirit, the memoirs of Hardy [1, pp.
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New Numerical Approach for Solving Abel’s Integral Equations
Foundations of Computing and Decision Sciences, 2021 Abstract In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then ...
Şenel Anapalı, Ayşe +2 more
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On a class of nonlocal problems for hyperbolic equations with degeneration of type and order
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 Nonlocal problems for the second order hyperbolic model equation were studied in the characteristic area. The type and order of equations degenerate on the same line $y = 0$.
Oleg A Repin, Svetlana K Kumykova
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Solution of the Generalized Abel Integral Equation [PDF]
Journal of Integral Equations and Applications, 2008 This paper presents a direct method for solving (in closed form) a generalized Abel integral equation.
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The boundary value problem with data given on the parallel characteristics for the system of hyperbolic equations with the wave operator and the singular matrix coefficient at the lower derivative is considered in the characteristic square.
Rina Rinatovna Rayanova
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