ON THEOREMS CONNECTING THE LAPLACE TRANSFORM AND A GENERALIZED FRACTIONAL INTEGRAL OPERATOR

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K. C. GUPTA
S. P. GOYAL
TARIQ O. SALIM

Abstract




The aim of the present paper is to establish two theorems connecting the Laplace transform and a certain class of generalized fractional integral operators involving a generalized polynom叫 set. These theorems provide .usful extension and unification of a number of (known or new) results for vaious classes of fractional integral operators. Several interesting applications of the main theorems are also mentioned briefly.




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GUPTA, K. C., GOYAL, S. P., & SALIM, T. O. (1998). ON THEOREMS CONNECTING THE LAPLACE TRANSFORM AND A GENERALIZED FRACTIONAL INTEGRAL OPERATOR. Tamkang Journal of Mathematics, 29(4), 323–333. https://doi.org/10.5556/j.tkjm.29.1998.4261
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Papers

References

S. N. Agal and C. L. Koul, "Weyl fractional calculus and Laplace transform," Proc. Indian Acad. Sci. {Math. Sci.), 92(1983), 167-170.

B. D. Agrawal and J. P. Chaubey, "Operational derivation of generating relations for gen­ eralized polynomials," Indian J. Pure Appl. Math., 11(1980), 1155-1157; ibid. 11 (1981), 357-379.

R. Agrawal, R. S. Pareek and M. Saigo, "A general fractional integral formula," J. Fractional Calculus, 7(1995), 55-60.

S. K. Chatterjea, "Qulques fonctions generatrices des polynomes d'Hermite, du point de vue de lalgebre de Lie," C. R. Acad. Sci Paris Ser. A-B, 268(1969), A 600-602.

H. W. Gould and A. T. Hopper, "Operational formulas connected with two generalizations of Hermite polynomials," Duke Math. J., 29(1962), 51-63.

K. C. Gupta and R. C. Soni, "On unified fractional integral operators," Proc. Indian Acad. Sci. {Math. Sci.), 106(1996), 53-64,

H. L. Krall and 0. Frink, "A new class of orthogonal polynomials: the Bessel polynomials," Trans. Amer. Math. Soc., 65(1949), 100-115.

N. W. McLachlan, Modern Operational Calculus with Applications in Technical Mathemat­ics, Macmillan, London, 1948.

S. K. Raizada, A study of unified representation of special functions of mathematical physics and their use in statistical and boundary value problems, Ph. D thesis, Bundlkhand Univ., India, 1991.

M. Saigo, "A remark on integral operators involving the Gauss hypergeometric functions," Math. Rep. College General Ed. Kyushu Univ., 11(1978), 135-143.

M. Saigo and R. K. Raina, "Fractional Calculus operators associated with a general class of polynomials," Fukuoka Univ. Sci. Rep., 18(1988), 15-22.

M. Saigo, S. P. Goyal and S. Saxena, "A theorem relating a generalized Weyl fractional in­tegral, Laplace and Varma transforms with applications," J. Fractional Calculus, 13(1998), 43-56.

R. K. Saxena and R. K. Kumbat, "Integral operators involving H-function," Indian J. pure. Appl. math., 5(1974), 1-6.

R. K. Singh and K. N. Shrivastava, "A note on generalization .of Laguerre and Humbert polynomials," Ricerca {Napoli), 14 (2)(1963), 11-21, Errata, Ibid, 15(1964), 63.

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Wiley/Halsted, New York, 1984.

H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-Functions of One and Two Variables with Applications, South Asian Pubishers, New Delhi-Madras, 1982.

H. M. Srivastava and R. Panda, "on the unified presentation of certain classical polynomi­als," Boll. Un. Mat. Ital., 12(4)(1975), 306-314.

H. M. Srivastava, M. Saigo and R. K. Raina, "Some existence and connection theorems associated with the Laplace transform and a certain class of integral operators," J. Math. Anal. Appl., 172(1993), 1-10.

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