A Study of Fractional Calculus Operators and Integrals...

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A Study of Fractional Calculus Operators and Integrals Pertaining to Certain Special Functions with Applications SBA Poornima University, Jaipur May, 2015 Page 186 References [1] A. Ansari, Fractional exponential operators and time-fractional telegraph equation, Springer, 2012. URL - http://www.boundaryvalueproblems.com/content/2012/1/125. [2] A. Erd´elyi, On some functional transformations, Rend. Semin. Mat. Univ. Politec. Torino, 10 (1950-51), 217- 234. [3] A. Erdélyi, Beitrag zur theorie der konfluenten hypergeometrischen funktionen von mehreren veränderlichen, S-B. Akad. Wiss. Wien. Abt. II a Math.-Natur, K1., 146 (1937), 431-467. [4] A. Erdélyi, Transformation of hypergeometric integrals by means of fractional integration by parts, Ibid.,10 (1939), 176-189. [5] A. Erdélyi, Integraldarstellungen fur produkte Whittakerscher funktionen, Nieuw Arch. Wisk., (2) 20 (1939), 1- 34. [6] A. Erdélyi, On fractional integration and its applications to the theory of Hankel transforms, Quart. J. Math. (Oxford), 11 (1940), 293-303. [7] A. Erdélyi, An application of fractional integrals, J. Analye Math., 14 (1965), 113-126. [8] A. Erde´lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, Vol I. McGraw-Hill, New York (1953) [9] A. Erde´lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, Vol II. McGraw-Hill, New York (1953) [10] A. Faraj, T. Salim, S. Sadek and J. Smail, Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators, Hindawi Publishing Corporation Journal of Mathematics, Volume 2013, Article ID 821762, 5 pages. URL - http://dx.doi.org/10.1155/2013/821762 [11] A. Parashar, A study of certain new aspect of differ-integral operators, general sequence of functions and general class of H-functions. Ph.D. thesis, University of Rajasthan, Jaipur, India (2002). [12] A. Zygmund, Theorem on fractional derivatives, Duke Math. J., 12(1945), 455-464. [13] A. A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynman integrals: I. Transformation and reduction formulae, J. Phys. A. Math. Gen. 20 (1987), 4109 4117. [14] A. A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynmann integrals: II. A generalization of the H-function, J. Phys. A: Math. Gen., 20 (1987), 4119- 4128. [15] A. A. Kilbas, Fractional calculus of the generalized Wright function, Fract. Calc. Appl. Anal. 8 (2), (2005), 113126. [16] A. A. Kilbas and M. Saigo, On generalized fractional integration operators with Fox’s H-function on spaces FP, and ' P, F , Integral Transforms and Special Functions, 4N-2 (1996), 103-114. [17] A. A. Kilbas and M. Saigo, Fractional calculus of the H-function, Fukuoka Univ. Sci. Rep., 28 (1998), 41-51. [18] A. A. Kilbas and M. Saigo, H-transforms, theory and applications, Chapman & Hall/CRC Press, Boca Raton, FL. 2004.

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A Study of Fractional Calculus Operators and Integrals Pertaining to Certain Special Functions with

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Poornima University, Jaipur May, 2015 Page 186

References

[1] A. Ansari, Fractional exponential operators and time-fractional telegraph equation, Springer, 2012.

URL - http://www.boundaryvalueproblems.com/content/2012/1/125.

[2] A. Erd´elyi, On some functional transformations, Rend. Semin. Mat. Univ. Politec. Torino, 10 (1950-51), 217-

234.

[3] A. Erdélyi, Beitrag zur theorie der konfluenten hypergeometrischen funktionen von mehreren veränderlichen,

S-B. Akad. Wiss. Wien. Abt. II a Math.-Natur, K1., 146 (1937), 431-467.

[4] A. Erdélyi, Transformation of hypergeometric integrals by means of fractional integration by parts, Ibid.,10

(1939), 176-189.

[5] A. Erdélyi, Integraldarstellungen fur produkte Whittakerscher funktionen, Nieuw Arch. Wisk., (2) 20 (1939), 1-

34.

[6] A. Erdélyi, On fractional integration and its applications to the theory of Hankel transforms, Quart. J. Math.

(Oxford), 11 (1940), 293-303.

[7] A. Erdélyi, An application of fractional integrals, J. Analye Math., 14 (1965), 113-126.

[8] A. Erde´lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, Vol I.

McGraw-Hill, New York (1953)

[9] A. Erde´lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, Vol II.

McGraw-Hill, New York (1953)

[10] A. Faraj, T. Salim, S. Sadek and J. Smail, Generalized Mittag-Leffler Function Associated with Weyl

Fractional Calculus Operators, Hindawi Publishing Corporation Journal of Mathematics, Volume 2013, Article ID

821762, 5 pages.

URL - http://dx.doi.org/10.1155/2013/821762

[11] A. Parashar, A study of certain new aspect of differ-integral operators, general sequence of functions and

general class of H-functions. Ph.D. thesis, University of Rajasthan, Jaipur, India (2002).

[12] A. Zygmund, Theorem on fractional derivatives, Duke Math. J., 12(1945), 455-464.

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Transformation and reduction formulae, J. Phys. A. Math. Gen. 20 (1987), 4109–4117.

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generalization of the H-function, J. Phys. A: Math. Gen., 20 (1987), 4119- 4128.

[15] A. A. Kilbas, Fractional calculus of the generalized Wright function, Fract. Calc. Appl. Anal. 8 (2), (2005),

113–126.

[16] A. A. Kilbas and M. Saigo, On generalized fractional integration operators with Fox’s H-function on spaces

FP, and '

P ,F

, Integral Transforms and Special Functions, 4N-2 (1996), 103-114.

[17] A. A. Kilbas and M. Saigo, Fractional calculus of the H-function, Fukuoka Univ. Sci. Rep., 28 (1998), 41-51.

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FL. 2004.

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Applications SBA

Poornima University, Jaipur May, 2015 Page 187

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