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Stability analysis for a nonlinear coupled system of fractional hybrid delay differential equations
Author(s) -
Ahmad Israr,
Shah Kamal,
Rahman Ghaus,
Baleanu Dumitru
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6526
Subject(s) - mathematics , stability (learning theory) , nonlinear system , differential equation , fixed point , work (physics) , mathematical analysis , computer science , mechanical engineering , physics , quantum mechanics , machine learning , engineering
The main objective of this research work is to establish existence results as well as to study qualitative aspects of the proposed coupled system of fractional hybrid delay differential equations (FHDDEs). Using the hybrid fixed point theory, we establish appropriate results for the existence of at least one solution to our problem. The powerful tools of functional analysis and dynamical systems are applied to derive different kinds of stability analysis. These include Ulam‐Hyers (UH), generalized Ulam‐Hyers (GUH), Ulam‐Hyers‐Rassias (UHR), and generalized Ulam‐Hyers‐Rassias (GUHR). In order to provide the authenticity of the our results, an illustrative example is given to wind up the present research work.