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On the Fractional Calculus Operators and DefiniteResults Including N2-Function

Mohd. Farman Ali, Manoj Sharma, Renu Jain

Abstract


In this present paper, fractional Riemann-Liouville calculus operators of a new special function called N2-function is introduced given by author has been obtained. This function is a modified form of Mittag-Leffler function [1]. The author drives the results between N2-function and fractional operators.

 

Cite this Article:
Mohd. Farman Ali, Manoj Sharma, Renu Jain. On the Fractional Calculus Operators and Definite Results Including N2-Function. Research & Reviews: Discrete Mathematical Structures. 2015; 2(2): 5–9p.


Keywords


Riemann-liouville fractional integral and derivative operators, N2-function, special functions.

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References


Mittag-Leffler G.M.. Sur la nouvelle function

Fox C., The G and H- function as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 1961; 98:395–429p.

Mathai A. M., Saxena R. K.. Tha H-function with Application in Statistics and Other Disciplines. John Wiley and Sons, Inc., New York. 1978.

Inayat Hussain A. A.. New properties of hypergeometric series derivable from Feynman integrals. II: A generalization of

Prudnikov A. P., BBrychkov Yu., Marichev O. I.. Integrals and Series. More Special Functions. Gordon and Breach, New York NJ. 1990; 3.

Samko S., Kilbas A., Marichev O. Fractional Integrals and derivaties. Theory and Applications. Gordon and Breach, New York. 1993.

Grenflo R. and Mainardi F. the Mittag-Leffler function in Reimann-Liouville fractional calculus, Kilbas, A. A. (ed.) Boundary value Problems. Special function and fractional calculus (Proc. Int. conf. Minsk 1996) Belarusian state University, Minsk. 1996: 215–225p.

Podlubny I. Fractional Differential Equations. Acad. Press, San Diego- New, York. 1999.

Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and Applications of Fractional Differential Equations. Elsevier, North Holland Math. Studies 204, Amsterdam, etc. 2006.

Kiryakova V. some special functions related to fractional calculus and fractional (non-integer) order control systems and equations. Facta Universitatis (Sci. J. of Univ. Nis) Automatic Control and Robotics. 2008; 7(1): 79–98p.

Sharma, M. Fractional Integration and Fractional Differentiation of the M-Series. J. Fract. Calc. and Appl. Anal. 2008; 11(2): 187–191p.

Sharma, M. and Jain, R. A note on a generalized M-Series as a special function of fractional calculus. J. Fract. Calc. and Appl. Anal. 2009; 12(4): 449–452p.

Sexena R. K. A remark on a paper on M-series. Fract. Calc. Appl. Anal. 2009; 12(1): 109–110p.

Kiryakova V. The special functions of fractional calculus as generalized fractional calculus operators of some basic functions. Computers and Math. with Appl. 2010; 59.

Abramowitz, M., Stegun, I. A.: Handbook of Mathematical functions. Dover, New York. 1965.


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