On a new class of \(\Phi \)-Caputo-type fractional differential Langevin equations involving the p-Laplacian operator

This paper aims to investigate the existence result for a new class of \(\Phi \) $\mathrm{\Phi }$ -Caputo-type fractional differential Langevin equation involving the p-Laplacian operator. We develop these result with the help of the theory of p-Laplacian operator, and by making use of some basic proprieties of fractional calculus. By applying Schaefer’s fixed point theorem, we established the existence result. As application, we give an example to demonstrate our theoretical result.