A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

• Published in: Acta mathematica scientia Vol. 35; no. 6; pp. 1386 - 1400
• Main Authors: SRIVASTAVA, H.M., LUO, Minjie, RAINA, R.K.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2015; Department of Mathematics and Statistics, University of Victoria,Victoria, British Columbia V8W 3R4, Canada%Department of Mathematics, East China Normal University, Shanghai 200241, China%Department of Mathematics, M.P.University of Agriculture and Technology,Udaipur 313001, Rajasthan, India
• Subjects: 33C60; 44A10; 44A20; al型; Borel-Džrbashjan transform; existence theorem; Fubini's theorem; H-function; H-transform; Heaviside generalized function; H变换; inversion formula; Laplace transform; natural transform; Parseval-type relationship; Sumudu transform; Weierstrass's test; 反演公式; 存在性定理; 应用; 微分方程; 积分变换; 积分恒等式; H-function; Parseval-type relationship; existence theorem; natural transform; Fubini's theorem; 44A20; Borel-Džrbashjan transform; inversion formula; Heaviside generalized function; 44A10; Weierstrass's test; 33C60; Laplace transform; Sumudu transform; H-transform; invcrsion formula; Borel-D(z)rbashjan transform
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(15)30061-8

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, in- clude （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.