참고문헌
- P. Agarwal, M. Chand, and E. T. Karimov, Certain image formulas of genearlized hypergeometric functions, Appl. Math. Comput. 266 (2015), 763-772.
- P. Agarwal and J. Choi, Fractional calculus operators and their image formulas, J. Korean Math. Soc. 53 (2016), no. 5, 1183-1210. https://doi.org/10.4134/JKMS.j150458
- P. Agarwal, J. Choi, K. B. Kachhia, J. C. Prajapati, and H. Zhou, Some Integral Trans-forms and Fractional Integral Formulas for the Extended Hypergeometric Functions, Commun. Korean Math. Soc. 31 (2016), no. 3, 591-601. https://doi.org/10.4134/CKMS.c150213
- A. Carpinteri and F. Mainardi, Fractals and Fractional Calculus in Physics, Springer, Vienna, 1997.
- J. Choi, K. B. Kachhia, J. C. Prajapati, and S. D. Purohit, Some integral transforms involving extended generalized Gauss hypergeometric functions, Commun. Korean Math. Soc. 31 (2016), no. 4, 779-790. https://doi.org/10.4134/CKMS.c150242
- L. Galue, A. Al-Zamel, and S. L. Kalla, Further results on generalized hypergeometric functions, Appl. Math. Comput. 136 (2003), no. 1, 17-25. https://doi.org/10.1016/S0096-3003(02)00014-0
- R. Hilfer, Applications of Fractional Calculus in Physics, World scientific, Singapore, 2000.
- I. S. Jesus and J. A. T Machado, Fractional control of heat diffusion systems, Nonlinear Dynam. 54 (2008), no. 3, 263-282. https://doi.org/10.1007/s11071-007-9322-2
- K. B. Kachhia and J. C. Prajapati, Solution of fractional partial differential equation aries in study of heat transfer through diathermanous material, J. Interdisciplinary Math. 18 (2015), no. 1-2, 125-132. https://doi.org/10.1080/09720502.2014.996017
- K. B. Kachhia and J. C. Prajapati, On generalized fractional kinetic equations involving generalized Lommel-Wright functions, Alexandria Engineering J. 55 (2016), 2953-2957. https://doi.org/10.1016/j.aej.2016.04.038
- V. Kiryakova, Generalized Fractional Calculus and Applications, Wiley and Sons Inc., New York, 1994.
- V. Kiryakova, On two Saigo's fractional integral operators in the class of univalent functions, Fract. Cal. Appl. Anal. 9 (2006), no. 2, 161-176.
- A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-Functions: Theory and Appli-cations, Springer, New York, 2010.
-
R. K. Parmar and R. K. Saxena, The incomplete generalized
$\tau$ -hypergeometric and second -Appell functions, J. Korean Math. Soc. 53 (2016), no. 2, 363-379. https://doi.org/10.4134/JKMS.2016.53.2.363 - I. J. Podulbuny, Fractional Differential Equations, Academic Press, New York, 1999.
- T. Pohlen, The Hadamard Product and Universal Power Series, Dissertation, Univer-sitat Trier, 2009.
- J. C. Prajapati and K. B. Kachhia, Fractional modeling of temperature distribution and heat flux in the semi infinite solid, J. Fract. Cal. Appl. 5 (2014), no. 2, 38-43.
- J. C. Prajapati, K. B. Kachhia, and S. P. Kosta, Fractional Calculus Approach to Study Temperature Distribution Within a Spinning Satellite, Alexandria Engineering J. 55 (2016), 2345-2350. https://doi.org/10.1016/j.aej.2016.05.004
- E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx-New York, 1971.
- M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. College of General Edu. Kyushu University 1 (1978), 135-143.
- I. N. Sneddon, The Use of Integral Transform, Tata McGraw-Hill, New Delhi, India, 1979.
- H. M. Srivastava and R. P. Agarwal, Certain Fractional Integral Operators and the Generalized Incomplete Hypergeometric Functions, Int. Appl. Math. 8 (2013), no. 2, 333-345.
- H. M. Srivastava, M. A. Chaudhary, and R. P. Agarwal, The incomplete Pochham-mer symbols and their applications to hypergeometric and relative functions, Integral Transforms Spec. Funct. 23 (2012), no. 9, 659-683. https://doi.org/10.1080/10652469.2011.623350
- H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science, Amsterdam, The Netherlands, 2012.
- N. Virchenko, S. L. Kalla, and A. Al-Zamel, Some results on a generalized hypergeomet-ric function, Integral Transforms Spec. Funct. 12 (2001), no. 1, 89-100. https://doi.org/10.1080/10652460108819336