Riemann–Liouville q -Fractional Calculi
作者： Mahmoud H. Annaby , Zeinab S. Mansour
DOI: 10.1007/978-3-642-30898-7_4
关键词:
摘要: In this chapter we investigate q-analogues of the classical fractional calculi. We study q-Riemann–Liouville integral operator introduced by Al-Salam (Proc. Am. Math. Soc. 17, 616–621, 1966; Proc. Edinb. 2(15), 135–140, 1966/1967) and Agarwal Camb. Phil. 66, 365–370, 1969). give rigorous proofs existence q-integral q-derivative. Therefore establish a q-analogue Abel’s equation its solutions.
springer.com
sci-hub.st 参考文章(236)
Mohamed A Khamsi, William A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory ,(2001)
Victor G. Kac, Alberto De Sole, On integral representations of $q$-gamma and $q$-beta functions Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni. ,vol. 16, pp. 11- 29 ,(2005)
Sunil Dutt Purohit, SUMMATION FORMULAE FOR BASIC HYPERGEOMETRIC FUNCTIONS VIA FRACTIONAL q-CALCULUS Le Matematiche. ,vol. 64, pp. 67- 75 ,(2010)
Hari M Srivastava, Anatoly A Kilbas, Juan J Trujillo, Theory and Applications of Fractional Differential Equations ,(2006)
Jean Paul Bézivin, Abdelbaki Boutabaa, Sur les équations fonctionelles $p$-adiques aux $q$-différences Collectanea Mathematica. ,vol. 43, pp. 125- 140 ,(1992)
Ahmed Fitouhi, Akram Nemri, Polynomial expansions for solution of wave equation in quantum calculus Le Matematiche. ,vol. 65, pp. 73- 82 ,(2010)
B.N. Narahari Achar, John W. Hanneken, David M. Vaught, Distribution of Zeros of the Mittag-Leffler Function Bulletin of the American Physical Society. ,vol. 2003, ,(2008)
The transforms and applications handbook tah. ,(2000) , 10.1201/9781420036756
Richard L. Rubin, Duhamel solutions of non-homogeneous ²-analogue wave equations Proceedings of the American Mathematical Society. ,vol. 135, pp. 777- 785 ,(2006) , 10.1090/S0002-9939-06-08525-X
Néji Bettaibi, Rym H. bettaieb, $q$-Analogue of the Dunkl transform on the real line arXiv: Quantum Algebra. ,(2007)