Well-posedness of mixed fractional-order nonlocal Problems with absorption phenomena

Abstract

This paper proves the existence of entropy solutions for a generalized class of mixed fractionalorder systems (M-FOS) incorporating nonlocal operators and perturbation effects under Dirichlet boundary
conditions. We initiate our analysis under minimal regularity assumptions (treating f ∈ L1 data) and employ the Minty-Browder theorem to address non-coercive settings. By imposing structural conditions on the
perturbation term, we capture a broad spectrum of phenomena arising in physics, engineering, and biological
systems. Using variational techniques in fractional Sobolev spaces, we establish rigorous existence results for
the proposed model