Analysis of the family of integral equation involving incomplete types of I and (I)over-bar-functions

The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (I/F) and an incomplete (I) over bar -function ((I/F) over bar) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (I) over bar -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.

Automated summary

This article introduces and studies the Fredholm-type integral equation with an incomplete I-function and an incomplete I-bar-function in its kernel. The authors solve an integral problem involving IIF using fractional calculus and the Mellin transform principle. They then use the idea of the Mellin transform and fractional calculus to analyze an integral equation using the incomplete I-bar-function. Several important exceptional cases are discovered and investigated. The general discoveries in this article may lead to new integral equations and solutions that can help solve various real-world problems.