Coupled system of sequential partial σ (., .) Hilfer fractional differential equations with weighted double phase operator: Existence, Hyers-Ulam stability and controllability

Abstract

In this paper, we are concerned by a sequential partial Hilfer fractional differential system with weighted double phase operator. First, we introduce the concept of Hyers-Ulam stability with respect to an operator L for an abstract equation of the form u = LFu in Banach lattice by using the fixed-point arguments and spectral theory. Then, we prove the controllability and apply the previous results obtained for abstract equation to prove existence and Hyers- Ulam stability of a coupled system of sequential fractional partial differential equations involving a weighted double phase operator. Finally, an 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.  Mathematics Subject Classification (2010): 34B15, 34B16, 34B18