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INTEGRAL TRANSFORMS OF THE GALUE TYPE STRUVE FUNCTION

Yıl 2018, Cilt: 8 Sayı: 1, 114 - 121, 01.06.2018

Öz

This paper refers to the study of generalized Struve type function. Using generalized Galue type Struve function GTSF , we derive various integral transforms, including Euler transform, Laplace transform, Whittakar transform, K-transform and fractional Fourier transform. The transform images are expressed in terms of the gener- alized Wright function. Interesting special cases of the main results are also considered.

Kaynakça

  • Baricz, ´A., (2010), Generalized Bessel function of the first kind, In: Lect. Notes Math., Springer, Berlin.
  • Baricz, ´A, (2010), Geometric properties of Bessel functions, Publ. Math. Debrecen, 731(2), pp. 155-178.
  • Bhowmick,K.N., (1962), Some relations between generalized Struve function and hypergeometric func- tion, Vijnana Parishad Anusandhan Patrika, 5, pp.93-99.
  • Bhowmick,K.N., (1963), A generalized Struve function and recurrence formula, Vijnana Parishad
  • Anusandhan Patrika, (6), pp.01-11. Choi,J., Kachhia,K.B., Prajapati,J.C., and Purohit,S.D., (2016) Some integral transforms involving extended generalized Gauss hypergeometric functions, Commun. Korean Math. Soc., 31(4), pp.779
  • Chouhan,A., Purohit,S.D., and Saraswat,S., (2013) An alternative method for solving generalized differential equations of fractional order, Kragujevac J. Math., 37(2), pp.299306.
  • Erd´elyi,A., Magnus,W., Oberhettinger,F., and Tricomi,F.G., (1954), Higher Transcendental Func- tions, Vol.2, Mc Graw-Hill, New York.
  • Kanth,B.N., (1981), Integrals involving generalized Struve function, Nepali Math Sci. Rep, 6, pp.61-64.
  • Luchko,Y., Martinez,H., and Trujillo,J., (2008), Fractional Fourier transform and some of its applica- tion, Fract. Calc. Appl. Anal., 11(4), pp.457-470.
  • Mathai,A.M., Saxena,R.K., and Haubold,H.J., (2010), The H-function Theory and Application, Springer, New York.
  • Mondal,S.R. and Swaminathan,A., (2012), Geometric properties of generalized Bessel function, Bull.
  • Malays. Math. Sci. Soc., 35(1), pp. 179-194. Nisar,K.S., Baleanu,D., and Qurashi,M.M.A., (2016), Fractional calculus and application of general- ized Struve function, Springerplus 29;5(1):910. DOI 10.1186/s40064-016-2560-3.
  • Nisar,K.S., Purohit,S.D., and Mondal,S.R., (2016b), Generalized fractional kinetic equations involving generalized Struve function of first kind, J. King Saud Univ. Sci., 28(2), pp.161-167.
  • Orhan,H. and Yagmur,N., (2013), Starlike and convexity of generalized Struve function, Abstract Appl. Anal., Art. ID 954516:6.
  • Purohit,S.D., (2013), Solutions of fractional partial differential equations of quantum mechanics, Adva. Appl. Math. Mech., 5(5), pp.639-651.
  • Purohit,S.D. and Kalla,S.L., (2011), On fractional partial differential equations related to quantum mechanics, J. Phys. A: Math. Theor., 44(4), Art. ID 045202:8.
  • Singh,R.P., (1988), On definite integrals involving generalized Struve’s function, Math Ed (Siwan), , pp.62-66.
  • Singh,R.P., (1988), Some integral representation of generalized Struve’s function, Math Ed (Siwan), , pp.91-94.
  • Singh,R.P., (1989), Infinite integral involving generalized Struve function, Math Ed (Siwan), 23, pp.30
  • Sneddon,I.N., (1979), The use of Integral Transform, Tata Mc Graw Hill, New Delhi.
  • Srivastava,H.M. and Karlson,P.W., (1985), Multiple Gaussian Hypergeometric Series, Halsted Press
  • (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto. Wittaker,E.T. and Watson,G.N., (1962), A course of Modern Analysis, Cambridge University Press, Cambridge.
  • Wright,E.M., (1935), The asymptotic expansion of the generalized hypergeometric functions, J. Lon- don Math. Soc., 10, pp.286-293.
Yıl 2018, Cilt: 8 Sayı: 1, 114 - 121, 01.06.2018

Öz

Kaynakça

  • Baricz, ´A., (2010), Generalized Bessel function of the first kind, In: Lect. Notes Math., Springer, Berlin.
  • Baricz, ´A, (2010), Geometric properties of Bessel functions, Publ. Math. Debrecen, 731(2), pp. 155-178.
  • Bhowmick,K.N., (1962), Some relations between generalized Struve function and hypergeometric func- tion, Vijnana Parishad Anusandhan Patrika, 5, pp.93-99.
  • Bhowmick,K.N., (1963), A generalized Struve function and recurrence formula, Vijnana Parishad
  • Anusandhan Patrika, (6), pp.01-11. Choi,J., Kachhia,K.B., Prajapati,J.C., and Purohit,S.D., (2016) Some integral transforms involving extended generalized Gauss hypergeometric functions, Commun. Korean Math. Soc., 31(4), pp.779
  • Chouhan,A., Purohit,S.D., and Saraswat,S., (2013) An alternative method for solving generalized differential equations of fractional order, Kragujevac J. Math., 37(2), pp.299306.
  • Erd´elyi,A., Magnus,W., Oberhettinger,F., and Tricomi,F.G., (1954), Higher Transcendental Func- tions, Vol.2, Mc Graw-Hill, New York.
  • Kanth,B.N., (1981), Integrals involving generalized Struve function, Nepali Math Sci. Rep, 6, pp.61-64.
  • Luchko,Y., Martinez,H., and Trujillo,J., (2008), Fractional Fourier transform and some of its applica- tion, Fract. Calc. Appl. Anal., 11(4), pp.457-470.
  • Mathai,A.M., Saxena,R.K., and Haubold,H.J., (2010), The H-function Theory and Application, Springer, New York.
  • Mondal,S.R. and Swaminathan,A., (2012), Geometric properties of generalized Bessel function, Bull.
  • Malays. Math. Sci. Soc., 35(1), pp. 179-194. Nisar,K.S., Baleanu,D., and Qurashi,M.M.A., (2016), Fractional calculus and application of general- ized Struve function, Springerplus 29;5(1):910. DOI 10.1186/s40064-016-2560-3.
  • Nisar,K.S., Purohit,S.D., and Mondal,S.R., (2016b), Generalized fractional kinetic equations involving generalized Struve function of first kind, J. King Saud Univ. Sci., 28(2), pp.161-167.
  • Orhan,H. and Yagmur,N., (2013), Starlike and convexity of generalized Struve function, Abstract Appl. Anal., Art. ID 954516:6.
  • Purohit,S.D., (2013), Solutions of fractional partial differential equations of quantum mechanics, Adva. Appl. Math. Mech., 5(5), pp.639-651.
  • Purohit,S.D. and Kalla,S.L., (2011), On fractional partial differential equations related to quantum mechanics, J. Phys. A: Math. Theor., 44(4), Art. ID 045202:8.
  • Singh,R.P., (1988), On definite integrals involving generalized Struve’s function, Math Ed (Siwan), , pp.62-66.
  • Singh,R.P., (1988), Some integral representation of generalized Struve’s function, Math Ed (Siwan), , pp.91-94.
  • Singh,R.P., (1989), Infinite integral involving generalized Struve function, Math Ed (Siwan), 23, pp.30
  • Sneddon,I.N., (1979), The use of Integral Transform, Tata Mc Graw Hill, New Delhi.
  • Srivastava,H.M. and Karlson,P.W., (1985), Multiple Gaussian Hypergeometric Series, Halsted Press
  • (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto. Wittaker,E.T. and Watson,G.N., (1962), A course of Modern Analysis, Cambridge University Press, Cambridge.
  • Wright,E.M., (1935), The asymptotic expansion of the generalized hypergeometric functions, J. Lon- don Math. Soc., 10, pp.286-293.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

D.l. Suthar Bu kişi benim

S.d. Purohit Bu kişi benim

K.s. Nisar Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 1

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