The stability of n-dimensional linear fractional differential systems with commensurate order 1 < α < 2 and the corresponding perturbed systems is investigated. By using the Laplace transform, the asymptotic expansion of the Mittag-Leffler function, and the Gronwall inequality, some conditions on stability and asymptotic stability are given.

The power law has been used to construct the derivative with fractional order in Caputo and RiemannLiouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more ...

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We propose a method for determining the solution and source term of a generalized timefractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag–Leffler...

I generalize the standard notion of the composition g ◦ f of correspondences f : X → Y and g : Y → Z to the case that X and Z are arbitrary varieties but Y is smooth and projective. Using this notion, I give a short self-contained proof of Rost’s “nilpotence theorem” and a generalization of one important result used by Rost in his proof of the nilpotence theorem.

Symmetrizations of tensors by irreducible characters of the symmetric group serve as natural analogues of symmetric and skew-symmetric tensors. The question of when a symmetrized decomposable tensor is non-zero is intimately related to the rank partition of a matroid extracted from the tensor. In this paper we characterize the non-vanishing of the symmetrization of certain partially symmetrized...

The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion ) 0 ( R r   and a matrix ) (    r R being in perfect thermal contact at R r  is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 2 0   and , 2 0    respectively. The Laplace trans...