Solving Volterra Integral Equations Of Fraction Order Using Chebyshev Polynomials By Numerical Method
DOI:
https://doi.org/10.37376/fesj.vi16.7105Keywords:
Volterra integral-differential of the first and second kinds equations,, Abel’ integral equations, Chebyshev polynomials,, , Operational matrix.Abstract
This research paper deals with the numerical method for solving Voltaire integral equations of the first and second kind resulting from the Abel integral equation, as it included the study of the executive matrices of cheyshev polynomials and their use in solving some integral equations by transforming the integral equations volterra to a linear algebraic system.
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المراجع العربية:
د- سميرة الأمين محمد سليمان ,الدوال الخاصة ,منشورات مركز العلوم والتقنية للبحوث والدراسات ,2021.
د- معروف بسوت لليش ,المعادلات التكاملية وحساب التحويلات ,منشورات جامعة حلب ,كلية العلوم ,سوريا 2007-2008.
المراجع الأجنبية:
Azim Rivazl. Samane Jahan ara. Farzaneh Yousefi, Two-dimensional Chebyshev Polynomials for Solving Two-dimensional Integro-Differential Equations. Cankaya University Journal of Science and Engineering Volume 12, No. 2 (2015) 001–011.
A.M.Wazawaz,The combined laplace transform-Adomian decomposition method for handling nonlinear Volterra integro -differential equations,Appl.Math.comput.216(2010)13041309.
A.Nkwanta and E.R.BarnesTwo Catalan-type Riordan arrays and their connections to the Chebyshev polynomials of the first kind.Journal of Integer Sequences,15(2012)1-19.
FakhrodinMohammadi,Numerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative.Int. J. Adv. Appl. Math. andMech. ISSN: 2347-2529.2(1) (2014) 83 – 91.
Mohammadreza Ahmadi Darani. Mitra Nasiri,A fractional type of the Chebyshev polynomials for approxima-tion of solution of linear fractional differential equations,Computational Methods for Differential Equations http://cmde.tabrizu.ac.ir Vol. 1, No. 2, 2013, pp. 96-107.
Monireh Nosrati Sahlan . Hadi Feyzollahzadeh R,Operational matrices of Chebyshev polynomials for solving singular Volterra integral equations.Received: 25 November 2016 / Accepted: 10 March 2017.
M. El-Kady, Amaal El-Sayed,FRACTIONAL DIFFERENTIATION MATRICES FOR SOLVING FRACTIONAL ORDERS DIFFERENTIAL EQUATIONS.International Journal of Pure and Applied Mathematics Volume 84 No. 2 2013, 1-13.
Nieto, J.J., Okrasinski, W.:Existence, uniqueness, and approximation of solutions to some nonlinear diffusion problems. J. Math. Anal. Appl. 210(1), (1997)231–240.
Olagunju, A. S. Joseph Folake L.,Third-kind Chebyshev Polynomials Vr(x) in Collocation Methods of Solving Boundary value Problems.IOSR Journal of Mathematics (IOSRJM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 7, Issue 2 (Jul. - Aug. 2013), PP 42-47
Okrasinski. W, Vila, S , Determination of the interface position for some nonlinear diffusion problems. Appl. Math. Lett. 11(4),(1998) 85–89.
Shantanu Das, Functional Fractional Calculus,Doi10.1007/978-3-642-20545-3,ISBN 978-3-642-20544-6,2011 Springer-Verlin Heidelberg.
Zeilon, N.:Sur quelques points de la theorie de l’equation integrale d’Abel [On some points of the theory of integral equation of Abel type]. Arkiv. Mat. Astr. Fysik. 18, (1924)1–19.

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