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Linked References

1. R. Hilfer, Ed., Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ, USA, 2000. View at MathSciNet
2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006. View at MathSciNet
3. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
4. I. Podlubny, “Geometric and physical interpretation of fractional integration and fractional differentiation,” Fractional Calculus & Applied Analysis, vol. 5, no. 4, pp. 367–386, 2002. View at Zentralblatt MATH · View at MathSciNet
5. Y. Luchko, “Maximum principle for the generalized time-fractional diffusion equation,” Journal of Mathematical Analysis and Applications, vol. 351, no. 1, pp. 218–223, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. J. Duoandikoetxia, Fourier Analysis, American Mathematical Society, Providence, RI, USA, 2001.
7. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, no. 30, Princeton University Press, Princeton, NJ, USA, 1970. View at MathSciNet
8. T. Kato, “On the Cauchy problem for the (generalized) Korteweg-de Vries equation,” in Studies in Applied Mathematics, vol. 8 of Advances in Mathematics. Supplementary Studies, pp. 93–128, Academic Press, New York, NY, USA, 1983. View at Zentralblatt MATH · View at MathSciNet
9. C. E. Kenig, G. Ponce, and L. Vega, “On the (generalized) Korteweg-de Vries equation,” Duke Mathematical Journal, vol. 59, no. 3, pp. 585–610, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
10. C. E. Kenig, G. Ponce, and L. Vega, “Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle,” Communications on Pure and Applied Mathematics, vol. 46, no. 4, pp. 527–620, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
11. J. C. Saut and R. Temam, “Remarks on the Korteweg-de Vries equation,” Israel Journal of Mathematics, vol. 24, no. 1, pp. 78–87, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
12. V. Varlamov, “Semi-integer derivatives of the Airy functions and related properties of the Korteweg-de Vries-type equations,” Zeitschrift für Angewandte Mathematik und Physik, vol. 59, no. 3, pp. 381–399, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
13. V. Varlamov, “Fractional derivatives of products of Airy functions,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 667–685, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
14. V. Varlamov, “Differential and integral relations involving fractional derivatives of Airy functions and applications,” Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 101–115, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
15. V. Varlamov, “Riesz potentials for Korteweg-deVries solitons,” Zeitschrift für Angewandte Mathematik und Physik. In press.
16. R. C. Sharpley and V. Vatchev, “Analysis of the intrinsic mode functions,” Constructive Approximation, vol. 24, no. 1, pp. 17–47, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
17. V. Vatchev and R. Sharpley, “Decomposition of functions into pairs of intrinsic mode functions,” Proceedings of the Royal Society A, vol. 464, no. 2097, pp. 2265–2280, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
18. O. Vallée and M. Soares, Airy Functions and Applications to Physics, Imperial College Press, London, UK, 2004. View at MathSciNet
19. R. C. McPhedran, L. C. Botten, N.-A. P. Nicorovici, and I. J. Zucker, “Symmetrization of the Hurwitz zeta function and Dirichlet $L$ functions,” Proceedings of the Royal Society A, vol. 463, no. 2077, pp. 281–301, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
20. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford University Press, Glasgow, UK, 2nd edition, 1962.
21. M. Abramowitz and I. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Washington, DC, USA, 1964.
22. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001. View at MathSciNet
23. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Die Grundlehren der Mathematischen Wissenschaften, Band 52, Springer, New York, NY, USA, 1966. View at MathSciNet
24. P. Hartman, Ordinary Differential Equations, John Wiley & Sons, Baltimore, Md, USA, 1973. View at MathSciNet
25. M. L. Glasser, “A remarkable property of definite integrals,” Mathematics of Computation, vol. 40, no. 162, pp. 561–563, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
26. D. Zwillinger, Handbook of Differential Equations, Academic Press, New York, NY, USA, 1998.