Generalized fractional integrals of product of two H-functions and a general class of polynomials

References

• P. Agarwal, Fractional integration of the product of two H-functions and a general class of polynomials, Asian J. Appl. Sci. 5(3) (2012), pp. 144–153.
   Google Scholar
• D. Baleanu, P. Agarwal, and S.D. Purohit, Certain fractional integral formulas involving the product of generalized Bessel functions, Sci. World J. 2014 (2014), Article ID 567132, 9 pp.
   Google Scholar
• D. Baleanu and O.G. Mustafa, On the global existence of solutions to a class of fractional differential equations, Comput. Math. Appl. 59(5) (2010), pp. 1835–1841.
   Web of Science ®Google Scholar
• D. Baleanu, O.G. Mustafa, and R.P. Agarwal, On the solution set for a class of sequential fractional differential equations, J. Phys. A Math. Theor. 43(38) (2010), Article ID 385209.
   Web of Science ®Google Scholar
• D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, MA, 2012.
   Google Scholar
• A.A. Kilbas, Fractional calculus of the generalized Wright function, Fract. Calc. Appl. Anal. 8(2) (2005), pp. 113–126.
   Google Scholar
• A.A. Kilbas and M. Saigo, H-Transforms, Theory and Applications, Chapman & Hall/CRC Press, Boca Raton, FL, 2004.
   Google Scholar
• V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Res. Notes Math. Ser., Vol. 301, Longman Scientific & Technical, Harlow, 1994.
   Google Scholar
• D. Kumar and J. Daiya, Generalized fractional differentiation of the H¯-function involving general class of polynomials, Int. J. Pure Appl. Sci. Technol. 16(2) (2013), pp. 42–53.
   Google Scholar
• A.M. Mathai and R.K. Saxena, Distribution of a product and the structural setup of densities, Ann. Math. Statist. 4 (1969), pp. 1439–1448.
   Google Scholar
• A.M. Mathai, R.K. Saxena, and H.J. Haubold, The H-Function: Theorey and Applications, Springer, New York, 2010.
   Google Scholar
• K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, A Wiley Interscience Publication. John Wiley and Sons Inc., New York, 1993.
   Google Scholar
• T.R. Prabhakar, A singular integral equation with a generalized Mittag–Leffler function in the kernel, Yokohama Math. J. 19 (1971), pp. 7–15.
   Google Scholar
• S.D. Purohit, Solutions of fractional partial differential equations of quantum mechanics, Adv. Appl. Math. Mech. 5(5) (2013), pp. 639–651.
   Web of Science ®Google Scholar
• S.D. Purohit and S.L. Kalla, On fractional partial differential equations related to quantum mechanics, J. Phys. A Math. Theor. 44(4) (2011), Article ID 045202.
   PubMed Web of Science ®Google Scholar
• S.D. Purohit, D.L. Suthar, and S.L. Kalla, Marichev–Saigo–Maeda fractional integration operators of the Bessel function, Le Matematiche LXVII (2012), pp. 21–32.
   Google Scholar
• J. Ram and D. Kumar, Generalized fractional integration involving Appell hypergeometric of the product of two H-functions, Vijanana Prishad Anusandhan Patrika 54(3) (2011), pp. 33–43.
   Google Scholar
• J. Ram and D. Kumar, Generalized fractional integration of the ℵ-function, J. Rajasthan Acad. Phy. Sci. 10(4) (2011), pp. 373–382.
   Google Scholar
• M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep., College General Ed. Kyushu Univ. 11 (1978), pp. 135–143.
   Google Scholar
• M. Saigo and N. Maeda, More Generalization of Fractional Calculus, Transform Methods and Special Functions, Varna, Bulgaria, 1996, pp. 386–400.
   Google Scholar
• S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon et alibi, 1993.
   Google Scholar
• R.K. Saxena, J. Ram, and D. Kumar, Generalized fractional integration of the product of Bessel functions of the first kind, Proceeding of the 9th Annual Conference, SSFA, 9, 2010, pp. 15–27.
   Google Scholar
• R.K. Saxena, J. Ram, and D. Kumar, Generalized fractional differentiation of the Aleph-Function associated with the Appell function F3, Acta Cienc. Indica Math. 38(4) (2012), pp. 781–792.
   Google Scholar
• H.M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), pp. 1–6.
   Google Scholar
• H.M. Srivastava and N.P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo 32 (1983), pp. 157–187. doi: 10.1007/BF02844828
   Google Scholar
• H.M. Srivastava, K.C. Gupta, and S.P. Goyal, The H-functions of One and Two Variables with Applications, South Asian Publishers, New Delhi/Madras, 1982.
   Google Scholar