zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On right fractional calculus. (English) Zbl 1198.26006
Summary: Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of {\it J. A. Canavati} type [Nieuw Arch. Wiskd., IV. Ser. 5, 53--75 (1987; Zbl 0649.46026)] and their corresponding right fractional integrals.Then are given representation formulae of functions as fractional integrals of their above fractional derivatives, as well as of their right and left Weyl fractional derivatives.At the end, we mention some far reaching implications of our theory to mathematical analysis computational methods.Also we compare the right Caputo fractional derivative to right Riemann-Liouville fractional derivative. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
 26A33 Fractional derivatives and integrals (real functions)
Full Text:
References:
 [1] Anastassiou, G.: Quantitative approximations, (2001) · Zbl 0969.41001 [2] Canavati, J. A.: The Riemann -- Liouville integral, Nieuw archief voor wiskunde 5, No. 1, 53-75 (1987) · Zbl 0649.46026 [3] Kai Diethelm, Fractional differential equations. Available from: http://www.tu-bs.de/ diethelm/lehre/f-dgl02/fde-skript.ps.gz. · Zbl 1136.26302 [4] El-Sayed, A. M. A.; Gaber, M.: On the finite Caputo and finite Riesz derivatives, Electron J theor phys 3, No. 12, 81-95 (2006) [5] Frederico, G. S.; Torres, D. F. M.: Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem, Int math forum 3, No. 10, 479-493 (2008) · Zbl 1154.49016 [6] Gorenflo R, Mainardi F, Essentials of fractional calculus. Maphysto Center; 2000. Available from: http://www.maphysto.dk/oldpages/events/LevyCAC2000/MainardiNotes/fm2k0a.ps. · Zbl 1030.26004 [7] Miller, K. S.: The Weyl fractional calculus, Lecture notes in mathematics 457, 80-89 (1975) · Zbl 0305.44004 [8] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives, theory and applications, (1993) · Zbl 0818.26003