Pooseh, Shakoor; Almeida, Ricardo; Torres, Delfim F. M. Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative. (English) Zbl 1248.26013 Numer. Funct. Anal. Optim. 33, No. 3, 301-319 (2012). The authors obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of smooth functions. Their approach is to seek expansion formulae for the Hadamard fractional operators with integer order derivatives. Decomposition formulae for the left and right Hadamard fractional integrals are given, with approximation formulae and error estimations. Some examples are given to show the efficiency of such approximations. Reviewer: S. L. Kalla (Ellisville) Cited in 30 Documents MSC: 26A33 Fractional derivatives and integrals 33F05 Numerical approximation and evaluation of special functions Keywords:Hadamard fractional derivative; numerical approximations; fractional; expansion formulas PDFBibTeX XMLCite \textit{S. Pooseh} et al., Numer. Funct. Anal. Optim. 33, No. 3, 301--319 (2012; Zbl 1248.26013) Full Text: DOI arXiv References: [1] Andrews G. E., Special functions (1999) [2] Atanackovic T. M., Mech. Res. Comm. 35 (7) pp 429– (2008) · Zbl 1258.65103 · doi:10.1016/j.mechrescom.2008.05.003 [3] Butzer P. L., J. Math. Anal. Appl. 270 pp 1– (2002) · Zbl 1022.26011 · doi:10.1016/S0022-247X(02)00066-5 [4] Butzer P. L., Numer. Funct. Anal. Optim. 24 pp 673– (2003) · Zbl 1086.11014 · doi:10.1081/NFA-120026366 [5] Hadamard J., J. de Math. 4 (8) pp 101– (1892) [6] Katugampola U. N., Appl. Math. Comput. 218 pp 860– (2011) · Zbl 1231.26008 · doi:10.1016/j.amc.2011.03.062 [7] Kilbas A. A., J. Korean Math. Soc. 38 pp 1191– (2001) [8] Kilbas A. A., Theory and Applications of Fractional Differential Equations (2006) · Zbl 1138.26300 [9] Kilbas A. A., Math. Model. Anal. 12 pp 343– (2007) · Zbl 1132.26314 · doi:10.3846/1392-6292.2007.12.343-356 [10] Miller K. S., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993) · Zbl 0789.26002 [11] Podlubny I., Fractional Differential Equations (1999) · Zbl 0924.34008 [12] Samko S. G., Fractional Integrals and Derivatives (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.