Uneingeschränkter Zugang

Fredholm type integral equation with special functions


Zitieren

[1] P. Agarwal, J. Choi, R. B. Paris, Extended Riemann-Liouville fractional derivative operator and its application, J. Nonlinear Sci. Appl., 8 (2015), 451–466.10.22436/jnsa.008.05.01Search in Google Scholar

[2] D. Baleanu, P. Agarwal, S. D. Purohit, Certain fractional integral formulas involving the product of generalized Bessel functions, Sci. World J., (2013), 9 pages.10.1155/2013/567132386352224379745Search in Google Scholar

[3] D. Baleanu, D. Kumar, S. D. Purohit, Generalized fractional integration of the product of two H-functions and a general class of polynomials, Int. J. of Comp. Math., 93 (8) (2016), 1320–1329.10.1080/00207160.2015.1045886Search in Google Scholar

[4] R. G. Buchman, An inversion integral, Proc. Amer. Math. Soc. 13 (1962), 675–677.10.1090/S0002-9939-1962-0144156-3Search in Google Scholar

[5] M. A. Chaudhary, A. Qadir, M. Rafique, S. M. Zubair, Extension of Eulers beta function, Appl. Math. Comput. 159 (2) (2004), 589–602.Search in Google Scholar

[6] M. A. Chaudhary, A. Qadir, H. M. Srivastava, R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, J. Comput. Appl. Math. 78 (1) (1997), 19–32.Search in Google Scholar

[7] V. B. L. Chaurasia, V. Gill, Extension of integral equations of Fredholm type involving special function, Thai Journal of Mathematics, article in press (2017).Search in Google Scholar

[8] V. B. L. Chaurasia, D. Kumar, On the solutions of integral equations of Fredholm type with special functions, Tamsui Oxf. J. Math. Sci., 28 (1) (2012), 49–61.Search in Google Scholar

[9] V. B. L. Chaurasia, G. C. Olkha, Series representation for the H-function of several complex variables, The Math. Edu., 19 (1) (1985), 38–40.Search in Google Scholar

[10] T. P. Higgins, A hypergeometric function transform, J. Soc. Industr. Appl. Math., 12 (1970), 142–148.10.1017/S1446788700006339Search in Google Scholar

[11] A. A Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematical Studies, Elsevier Science, Amsterdem, The Netherlands, 2006.Search in Google Scholar

[12] D. Kumar, S. D. Purohit, J. Choi, Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials, J. Nonlinear Sci. Appl., 9 (2016), 8–21.10.22436/jnsa.009.01.02Search in Google Scholar

[13] D. Kumar, S. D. Purohit, A. Secer, A. Atangana, On generalized fractional kinetic equations involving generalized Bessel function of the first kind, Math. Probl. Eng., 2015 (2015), Article ID 289387, 7 pages.10.1155/2015/289387Search in Google Scholar

[14] H. Laurent, Sur Le calcul derives a indices quelconques, Nouv. Ann. Math., 3 (3) (1884), 240–252.Search in Google Scholar

[15] D. M. Lee, A. K. Rathie, R. K. Parmar, Y. S. Kim, Generalization of extended beta function, hypergeometric and confluent hypergeometric functions, Honam Math. J., 33 (2) (2011), 187–206.10.5831/HMJ.2011.33.2.187Search in Google Scholar

[16] E. R. Love, Some integral equations hypergeometric functions, Proc. Edinburgh Math. Soc., 15 (2) (1967), 169–198.10.1017/S0013091500011706Search in Google Scholar

[17] E. R. Love, A hypergeometric integral equation in fractional calculus and its applications, Edited by B. Ross, Springer-Verlag, New York, (1975), 272–288.10.1007/BFb0067112Search in Google Scholar

[18] R. K. Parmar, A new generalization of Gamma, Beta, hypergeometric and confluent hypergeometric functions, Matematiche (Catania), 68 (2) (2013), 33–52.Search in Google Scholar

[19] R. K. Parmar, Some generating relations for generalized extended hypergeometric functions involving generalized fractional derivative operator, J. Concr. Appl. Math., 12 (2014), 217–228.Search in Google Scholar

[20] T. R. Prabhakar, N. K. Kashyap, A new class of hypergeometric integral equations, Indian J. pure Appl. Math., 11 (1980), 92–97.Search in Google Scholar

[21] Y. N. Prasad, Multivariable I-function, Vijnana Parishad Anusandhan Patrika, 29 (1986), 231–235.Search in Google Scholar

[22] S. D. Purohit, S. L. Kalla, D. L. Suthar, Fractional integral operators and the multiindex Mittag-Leffler functions, Sci. Ser. A. Math. Sci., 21 (2011), 87–96.Search in Google Scholar

[23] S. D. Purohit, D. L. Suthar, S. L. Kalla, Marichev-Saigo-Maeda fractional integration operators of the Bessel function, Matematiche (Catania), 67 (2012), 21–32.Search in Google Scholar

[24] J. Ram, D. Kumar, Generalized fractional integration involving Appell hypergeometric of the product of two H-functions, Vijnana Parishad Anusandhan Patrika, 54 (2011), 33–43.Search in Google Scholar

[25] R. K. Saxena, J. Ram, D. Kumar, Generalized fractional integration of the product of Bessel functions of the first kind, Proceedings of the 9th Annual Conference, Soc. Spec. Funct. Appl., 9 (2011), 15–27.Search in Google Scholar

[26] J. B. Sharma, K. K. Sharma, S. D. Purohit, A. Antagana, Hybrid Water-marking Algorithm using Finite Radon and Fractional Fourier Transform, Fundamenta Informaticae, 151 (4) (2017), 523–543.10.3233/FI-2017-1508Search in Google Scholar

[27] H. M. Srivastava, A contour integral involving Fox’s H-function, Indian. J. Math., 14 (1972), 1–6.Search in Google Scholar

[28] H. M. Srivastava, A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math., 177 (1985), 183–191.10.2140/pjm.1985.117.183Search in Google Scholar

[29] H. M. Srivastava, R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables, Comment. Math. Univ. St. Paul., 24 (1975), 119–137.Search in Google Scholar

[30] H. M. Srivastava, R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables II, Comment. Math. Univ. St. Paul., 25 (1976), 167–197.Search in Google Scholar

[31] D. L. Suthar, R. K. Parmar, S. D. Purohit, Fractional calculus with complex order and generalized hypergeometric functions, Nonlinear Sci. Lett. A, 8 (2) (2017), 156–161.Search in Google Scholar

eISSN:
2066-7752
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
2 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines