Interrelationships Between Marichev–Saigo–Maeda Fractional Integral Operators, the Laplace Transform and the $${\overline{H}}$$-Function

Abstract

In this article, we first evaluate the Laplace transform of Marichev–Saigo–Maeda (M–S–M) fractional integral operators whose kernel is the Appell function $$F_{3}$$ and point out its six special cases (Saigo, Erdelyi–Kober, Riemann–Liouville and Weyl fractional integral operators). Certain new and known results can be obtained as special cases of our key findings. Next, we find the image of $${\overline{H}}$$ -Function under the operators of our study. Some interesting special cases of our key result are also considered and demonstrated to be connected with certain existing ones.