(p,q)-Laplacian Hilfer fractional differential system : Existence and Hyers-Ulam stability

Abstract

In this paper, we are concerned by existence and Hyers-Ulam stability of a generalized ($p,q$)-Laplacian Hilfer fractional differential system. First, we introduce the concept of Hyers-Ulam stability with respect to $\left(
L,F\right) $ for an abstract equation of the form $u=LFu$ in Banach lattice. Then, we establish sufficient conditions and employ the fixed point arguments and spectral theory to prove existence and Hyers-Ulam stability with respect to $\left( L,F\right) .$ Therefore, we apply the previous results to prove existence and Hyers-Ulam stability of a generalized ($p,q$%)-Laplacian Hilfer fractional differential system. Finally, example illustrating the main results is constructed. This work contains several new ideas, and gives a unified approach applicable to many types of differential equations.