Generalized Taylor’s formula

Applied Mathematics and Computation - Tập 186 Số 1 - Trang 286-293 - 2007
Zaid Odibat1, Nabil Shawagfeh2
1Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt, Jordan
2Department of Mathematics, University of Jordan, Amman, Jordan

Tóm tắt

Từ khóa


Tài liệu tham khảo

Mainardi, 1997, Fractional calculus: some basic problems in continuum and statistical mechanics, 291

Hardy, 1945, Riemann’s form of Taylor series, J. London Math., 20, 48, 10.1112/jlms/s1-20.1.48

I. Podlubny, The Laplace transform method for linear differential equations of fractional order, Slovac Academy of Science, Slovak Republic, 1994.

Podlubny, 1999

Truilljo, 1999, On a Riemann–Liouville generalized Taylor’s formula, J. Math. Anal., 231, 255, 10.1006/jmaa.1998.6224

Oldham, 1974

Diethelm, 2002, Analysis of fractional differential equations, J. Math. Anal. Appl., 265, 229, 10.1006/jmaa.2000.7194

Gorenflo, 1997, Fractional calculus: integral and differential equations of fractional order

Gorenflo, 1999, Analytical properties and applications of the Wrigth function, Fract. Calc. Appl. Anal., 2, 383

Bagley, 1990, On the fractional order initial value problem and its engineering applications, 12

Samko, 1993

Miller, 1993

Schneider, 1996, Completely monotone generalized Mittag–Leffler functions, Exposition. Math., 14, 3

Luchko, 1995, The exact solution of certain differential equations of fractional order by using operational calculus, Comput. Math. Appl., 29, 73, 10.1016/0898-1221(95)00031-S

Y. Wantanable, Notes on the generalized derivatives of Riemann–Liouville and its application to Leibntz’s formula, Thoku Math. J. 34, 28–41.