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INTEGRAL TRANSFORMS OF THE GALUE TYPE STRUVE FUNCTION

Year 2018, Volume: 8 Issue: 1, 114 - 121, 01.06.2018

Abstract

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.

References

  • 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.
Year 2018, Volume: 8 Issue: 1, 114 - 121, 01.06.2018

Abstract

References

  • 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.
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

D.l. Suthar This is me

S.d. Purohit This is me

K.s. Nisar This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

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