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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 3

A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel

Dumitru BALEANU
Ali H. BHRAWY
Mohamed A. ABDELKAWY
Ahmed Z. M. AMİN
Sayfa
553–566
Yayın Tarihi
2022-10-18
DOI
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Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper adapts a new numerical technique for solving two-dimensional fractional integral equations with weakly singular.
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Temel Bulgular & Veri:Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equations.
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Sonuç & Katkı:Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Two-dimensional fractional integral equations with weakly singular · Spectral collocation method · Gauss quadrature

Abstract

This paper adapts a new numerical technique for solving two-dimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equations. We apply the reported numerical method to solve several numerical examples in order to test the accuracy and validity. Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.

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Bu Makaleye Atıf Yap

BALEANU, D., BHRAWY, A. H., ABDELKAWY, M. A., AMİN, A. Z. M. (2022). A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 3, 553–566. https://ajindex.com/articles/529858

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Kaynakça (18)

  1. L.E. Kosarev, Applications of integral equations of the rst kind in experiment physics., Comput. Phys. Commun., 20 (1980) 69-75. H. Brunner, 1896-1996: One hundred years of Volterra integral equation of the rst kind, Appl. Numer. Math., 24 (1997) 83-93.
  2. A. M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer, Heidelberg, Dordrecht, London, New York, 2011.
  3. A. Wazwaz, A First Course in Integral Equations, World Scienti c Publishing, Singapore, 1997.
  4. A. Wazwaz, A reliable modi cation of Adomian decomposition method, Appl. Math. Comput., 102 (1999) 77-86.
  5. A. D. Polyanin and A.V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton, 1998.
  6. R. Metzler and J. Klafter, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A, 37 (2004) 161-208.
  7. R. T. Baillie, Long memory processes and fractional integration in econometrics, J. Econometrics, 73 (1996) 5-59.
  8. R. L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, 2006.
  9. D. A. Benson, S.W. Wheatcraft and M.M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resour. Res., 36 (2000) 1403-1412.
  10. S. Abbas and M. Benchohra, Fractional order integral equations of two independent variables, Appl. Math. Comput., 227 (2014) 755-761.
  11. S. Abbas and M. Benchohra, Fractional Order Riemann-Liouville Integral Equations with Multiple Time Delays, Applied Mathematics, 12 (2012) 79-87.
  12. R. Hilfer, Applications of Fractional Calculus in Physics, World Scienti c, Singapore, 2000.
  13. Y.L. Jiang and X.L Ding, Waveform relaxation methods for fractional dierential equations with the Caputo derivatives, J. Comput. Appl. Math., 238 (2013) 51-67.
  14. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Dierential Equations, Elsevier, 2006.
  15. H. Wang and N. Du, Fast alternating-direction nite dierence methods for threedimensional space-fractional diusion equations, J. Comput. Phys., 258 (2014) 305-318.
  16. J. Liu and G. Hou, Numerical solutions of the space- and time-fractional coupled Burgers equation by generalized dierential transform method, Appl. Math. Comput., 217 (2011) 7001-7008.
  17. L.Wang, Y. Ma and Z. Meng, Haar wavelet method for solving fractional partial dierential equations numerically, Appl. Math. Comput., 227 (2014) 66-76
  18. R.K. Pandey, O.P. Singh and V.K. Baranwal, An analytic algorithm for the space-time fractional advection-dispersi