Analysis of the family of integral equation involving incomplete types of I and Ī-functions. Issue 1 (31st December 2023)

• Record Type: Journal Article
• Authors: Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D. L.; Purohit, Sunil Dutt
• Is Part Of: Applied mathematics in science and engineering. Volume 31:Issue 1(2023)
• Publication Date: 2023-12-31
• Subjects: Fredholm-type integral equations -- IIF -- II¯F -- Mellin transform -- Weyl fractional integral; 33C60 -- 26A33 -- 33B20 -- 44A20 -- 45B05; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2023.2165280
• Languages: English
• ISSNs: 2769-0911

Abstract

ABSTRACT: The present article introduces and studies the Fredholm-type integral equation with an incomplete I -function (I I F) and an incomplete I ¯ -function (I I ¯ F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving I I F. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete I ¯ -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.