Stability analysis of distributed order of Hilfer nonlinear systems

For Hilfer derivatives of the product of two functions, we present equations and inequalities, generalizing well‐known results for Caputo and Riemann‐Liouville derivatives. Using the Laplace transformation, we introduce a generalized distributed Mittag‐Leffler‐Hilfer stability and show two results for like‐Lyapunov stability. We also extend equations and inequalities for the product of two functions of Hilfer derivatives of distributed order. Finally, we give some consequences and examples that illustrate the theory.

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