A Generalization of M-Series and Integral Operator Associated with Fractional Calculus
Keywords:
GeneralizedM-Series, H-function, Integral transforms, Fractional Integral and Differential OperatorsAbstract
WIll be available soonReferences
Fox, H., The G – and H-function as symmetric Fourier kernels. Trans. Amer. Math. Soc. 98, 395-429 (1961).
Hilfer, R ., Application of fractional calculus in physics. Singapore, New Jersy; London and HongKong. World scientific Publishing Company, (2000).
Inayat – Hussain, A., New properties of hypergeometric series derivable from Feynman integrals, II: Ageneralization of the H-function. J. Phys. A: Math. Gen. 20, 4119-4128 (1987).
Kilbas, A , and Saigo, M., H-transforms: Theory and applications, London, New York: Chapman and Hall/ CRS, (2004).
Kilbas, A , Saigo , M , and Sexena, R., Generalized Mittag-Leffler function and generalized fractional calculus operators. Integral Transforms Spec. Funct., Vol.15, 31-49 (2004).
Kilbas, A , Srivastava, H , and Trujillo, J., Theory and applications of fractional differential equations. Elsevier, North Holland Math. Studies 204, Amsterdam; etc, (2006).
Kiryakova, V., The special functions of fractional calculus as generalized fractional calculus operators of some basic functions. Comp. Math. Appl. 59( 3),1128-1141(2010).
Mathai, A , and Sexena, R ., The H-function with applications in statistics and other disciplines. John Wiley and Sons, New York (1978).
Prudnikov, A , Bbrychkov, Yu, and Marichev , O ., Integrals and Series. Vol.3: More special functions. Gordon and Breach, New York NJ (1990).
Rainville, E ., Special functions. New York: Chelsea Pulb. Co; (1960).
Salim, T, and Faraj, A ., A generalization of Mittag – Leffler function and integral operator associated with fractional calculus. J. Frac. Cal. appl. Vol.3, No.5, 1-13 (2012).
Samko, S, Kilbas, A and Marichev, O., Fractional Integrals and derivatives. Theory and applications. Gordon and Breach, Sci. Publ New York (1993).
Sexena, R ., A remark on a paper on M-series. Fract. Calc. Appl. Anal.12, No.1, 109-110 (2009).
Sharma, M., Fractional integration and fractional differentiation of the M-series. Fract. Calc. appl. Anal. 11, No.2, 187-192 (2008).
Sharma, M and Jain, R., A note on a generalized M-series as a special function of fractional calculus. Fract. Calc. appl. Anal. 12, No.4, 449-452 (2009).
Shukla, A , and Prajapati, J ., On a generalization of Mittag – Leffler function and its properties. J. Math. Appl. Anal. 336, 797-811 (2007).
Sneddon, I ., The use of integral transforms. Tata McGraw Hill .New Delhi , (1979).
Srivastava, H , and Manocha , H ., A treatise on generating functions. John Willy and Sons,New York , (1984).
Srivistave, H , and Tomovski, Z., Fractional calculus with an integral operator containing a generalized Mittag – Leffler function in the Kernel . Appl. Math. Comput., 211, 198-210 (2009).
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
