Abstract
In this paper, we study the stability and logarithmic decay of the solutions to fractional differential equations (FDEs). Both linear and nonlinear cases are included. And the fractional derivative is in the sense of Hadamard or Caputo–Hadamard with order $$\alpha \,(0<\alpha <1)$$ . The solutions can be expressed by Mittag–Leffler functions through applying the modified Laplace transform. In view of the asymptotic expansions of Mittag–Leffler function, we discuss the stability and logarithmic decay of the solution to FDEs in great detail.
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