Other q-Fractional Calculi

作者: Mahmoud H. Annaby , Zeinab S. Mansour

DOI: 10.1007/978-3-642-30898-7_5

关键词:

摘要: In this chapter we investigate q-analogues of some known fractional operators. This includes as well the generalization Askey–Wilson operator introduced in (Ismail and Rahman, J. Approx. Theor. 114(2), 269–307, 2002). At end introduce a q-difference (Rubin, Math. Anal. Appl. 212(2), 571–582, 1997).

参考文章(236)
Sergei K. Suslov, An introduction to basic Fourier series Kluwer Academic. ,(2003) , 10.1007/978-1-4757-3731-8
Predrag Rajkovic, Sladjana Marinkovic, Miomir Stankovic, On q–Analogues of Caputo Derivative and Mittag–Leffler Function Fractional Calculus and Applied Analysis. ,vol. 10, pp. 359- 373 ,(2007)
Richard B. Paris, D. Kaminski, Asymptotics and Mellin-Barnes Integrals ,(2001)
Tilak Raj Prabhakar, A SINGULAR INTEGRAL EQUATION WITH A GENERALIZED MITTAG LEFFLER FUNCTION IN THE KERNEL The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学. ,vol. 19, pp. 7- 15 ,(1971)
Kai Diethelm, Multi-Term Caputo Fractional Differential Equations Springer, Berlin, Heidelberg. pp. 167- 186 ,(2010) , 10.1007/978-3-642-14574-2_8
W. J. Trjitzinsky, Analytic theory of linear q -difference equations Acta Mathematica. ,vol. 61, pp. 1- 38 ,(1933) , 10.1007/BF02547785
Mizan Rahman, Qazi M. Tariq, Addition formulas for $q$-Legendre-type functions Methods and Applications of Analysis. ,vol. 6, pp. 3- 20 ,(1999) , 10.4310/MAA.1999.V6.N1.A1
Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales Birkhäuser Boston. ,(2001) , 10.1007/978-1-4612-0201-1
Joaquin Bustoz, Sergei K. Suslov, Basic analog of Fourier series on a $q$-quadratic grid Methods and Applications of Analysis. ,vol. 5, pp. 1- 38 ,(1998) , 10.4310/MAA.1998.V5.N1.A1