数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1386-1400.doi: 10.1016/S0252-9602(15)30061-8

• 论文 • 上一篇    下一篇

A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

H. M. SRIVASTAVA1, 罗旻杰2, R. K. RAINA3   

  1. 1. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada;
    2. Department of Mathematics, East China Normal University, Shanghai 200241, China;
    3. Department of Mathematics, M. P. University of Agriculture and Technology, Udaipur 313001, Rajasthan, India
  • 收稿日期:2015-04-01 修回日期:2014-08-12 出版日期:2015-11-01 发布日期:2015-11-01
  • 通讯作者: Minjie LUO, E-mail: mathwinnie@live.com E-mail:mathwinnie@live.com
  • 作者简介:H. M. SRIVASTAVA, E-mail: harimsri@math.uvic.ca;R. K. RAINA, E-mail: rkraina_7@hotmail.com

A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

H. M. SRIVASTAVA1, Minjie LUO2, R. K. RAINA3   

  1. 1. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada;
    2. Department of Mathematics, East China Normal University, Shanghai 200241, China;
    3. Department of Mathematics, M. P. University of Agriculture and Technology, Udaipur 313001, Rajasthan, India
  • Received:2015-04-01 Revised:2014-08-12 Online:2015-11-01 Published:2015-11-01
  • Contact: Minjie LUO, E-mail: mathwinnie@live.com E-mail:mathwinnie@live.com

摘要:

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, include (for example) existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

关键词: Laplace transform, Sumudu transform, natural transform, H-function, H-transform, inversion formula, Parseval-type relationship, existence theorem, Borel-D?, rbashjan transform, Fubini's theorem, Weierstrass's test, Heaviside generalized function

Abstract:

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, include (for example) existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

Key words: Laplace transform, Sumudu transform, natural transform, H-function, H-transform, inversion formula, Parseval-type relationship, existence theorem, Borel-D?, rbashjan transform, Fubini's theorem, Weierstrass's test, Heaviside generalized function

中图分类号: 

  • 33C60