| Summary: | The main aim of this article is to study the Fredholm-type integral equation involving the incomplete H-function (IHF) and incomplete <span style="text-decoration: overline;"><i>H</i></span>-function in the kernel. Firstly, we solve an integral equation associated with the IHF with the aid of the theory of fractional calculus and Mellin transform. Next, we examine an integral equation pertaining to the incomplete <span style="text-decoration: overline;"><i>H</i></span>-function with the help of theory of fractional calculus and Mellin transform. Further, we indicate some known results by specializing the parameters of IHF and incomplete <span style="text-decoration: overline;"><i>H</i></span>-function. The results computed in this article are very general in nature and capable of giving many new and known results connected with integral equations and their solutions hitherto scattered in the literature. The derived results are very useful in solving various real world problems.
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