Call for Paper - May 2015 Edition
IJCA solicits original research papers for the May 2015 Edition. Last date of manuscript submission is April 20, 2015. Read More
Fractional Calculus for Solving generalized Abel’s Integral Equations using Chebyshev Polynomials
International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 100 - Number 8
Year of Publication: 2014
|
10.5120/17545-8138 |
M H Saleh, S M Amer, Sh. D Mohamed and A E Mahdy. Article: Fractional Calculus for Solving generalized Abel's Integral Equations using Chebyshev Polynomials. International Journal of Computer Applications 100(8):18-23, August 2014. Full text available. BibTeX
@article{key:article,
author = {M. H. Saleh and S. M. Amer and D. Sh. Mohamed and A. E. Mahdy},
title = {Article: Fractional Calculus for Solving generalized Abel's Integral Equations using Chebyshev Polynomials},
journal = {International Journal of Computer Applications},
year = {2014},
volume = {100},
number = {8},
pages = {18-23},
month = {August},
note = {Full text available}
}
Abstract
In this paper we investigate the numerical solution of Abel's integral equations of the first and second kind by chebychev polynomials of the first ,second ,third and fourth kinds. Some numerical examples are presented to illustrate the method.
References
- A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Mathematics studies, Vol. 204, Elsevier, 2006. .
- A. D. Polyanin, A. V. Manzhirov, Handbook of Integral Equations, CRC Press, 2008.
- Abbas Saadatmandia, Mehdi Dehghanb, A Collocation Method for Solving Abel's Integral Equations of First and Second Kinds,Verlag der Zeitschrift fu¨r Naturforschung,752 -- 756 (2008).
- C. J. Cremers, R. C. Birkebak, Application of the Abel Integral Equation to Spectrographic Data, Appl. Opt. 5 (1966) 1057-1064.
- G. Capobianco, D. Conte, An efficient and fast parallel method for Volterra integral equations of Abel type, J. Comput. Appl. Math. 189 (2006) 481- 493.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
- J. C. Mason, D. C. Handscomb, Chebyshev Polynomials, CRC Press LLC, 2003.
- Johin Viley, Sons ,Inc, An introduction to the fractional calculus and fractional differential equations (1993).
- K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, NewYork, 1974.
- K. E. Atkinson, The Numerical Solutions of Integral Equations of the Second Kind, Cambridge University Press, 1997.
- K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations,Wiley, NewYork, 1993.
- L. Huang, Y. Huang, X. F. Li, Approximate solution of Abel integral equation, Comput. Math. Appl. 56 (2008) 1748-1757.
- M. Rahman, Integral Equations and Their Application, WITpress, 2007.
- R. Estrada, R. P. Kanwal, Singular Integral Equations, Springer, 2000.
- R. Gorenflo, S. Vessella, Abel Integral Equations: Analysis and Applications. Lecture Notes in Mathematics 1461, Springer-Verlag, Berlin, 1991.
- R. K. Pandey, O. P. Singh, V. K. Singh, Efficient algorithms to solve singular integral equations of Abel type, 57 (2009) 664-676.
- R. P. Agarwal, D. O'Regan, Singular Differential and Integral Equations with Applications, Springer, 2003.
- S. A. Yousefi, Numerical solution of Abel,s integral equation by using Legendre wavelets, Appl. Math. Comput. 175 (2006) 574-580.
- samah M. Dardery, Mohamed M. Allan, Chebyshev Polynomials for Solving a Class of Singular Integral Equations, Applied Mathematics, 2014, 5, 753-764.
- T. Miyakoda, Discretized fractional calculus with a series of Chebyshev polynomial, Electron. Notes Theor. Comput. Sci. 225 (2009) 239-244.
- V. Mirceski, Z. Tomovski, Analytical solutions of integral equations for modelling of reversible electrode processes under voltammetric conditions, J. Electroanal. Chem. 619-620 (2008) 164-168.
- Z. Avazzadeh, B. Shafiee and G. B. Loghmani, Fractional Calculus for Solving Abel's Integral Equations Using Chebyshev Polynomials, Applied Mathematical Sciences, Vol. 5, 2011, no. 45, 2207 - 2216.