Fréchet-Kolmogorov compactness of Prabhakar integral operator

چکیده مقاله

In many cases, the differential equations are converted into an equivalent functional equations involving integral operators generated by different kernels. The compactness property of the integral operators is often required for the existence of solutions for the corresponding differential equations. Our aim in this paper is to deal with Fréchet-Kolmogorov compactness of Prabhakar integral operator with Prabhakar-like memory kernel on Lebesgue spaces. Prabhakar-like function plays a crucial role in the derivation of the fundamental solutions for various fractional differential equations. © 2021, The Royal Academy of Sciences, Madrid.