Coupled system of sequential partial \(\sigma(.,.)\)-Hilfer fractional differential equations with weighted double phase operator: Existence, Hyers-Ulam stability and controllability
DOI:
https://doi.org/10.24193/subbmath.2024.4.09Keywords:
Control, sequential PDE, Hyers-Ulam stability, fixed pointAbstract
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 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, 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.References
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