Titlebook: Differential and Difference Equations with Applications; ICDDEA, Amadora, Por Sandra Pinelas,Zuzana Do?lá,Peter E. Kloeden Conference proce

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,Algebraic Properties of the Semi-direct Product of Kac–Moody and Virasoro Lie Algebras and AssociatWe discuss the semi-direct product of Virasoro and affine Kac–Moody Lie algebras and associated Verma modules, coadjoint orbits, Casimir functions, and bi-Hamiltonian systems.

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Complex-Valued Fractional Derivatives on Time Scales,We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.

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,Existence of Mild Solutions for Impulsive Fractional Functional Differential Equations of Order , ∈This paper investigates the existence result for fractional order functional differential equations subject to non-instantaneous impulsive condition by applying the classical fixed point technique. At last, an example involving partial derivatives is presented to verify the uniqueness result.

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Existence of the Mild Solutions for Nonlocal Fractional Differential Equations of Sobolev Type withfficient condition for providing the existence of mild solution to the nonlocal Sobolev-type fractional differential equation with iterated deviating arguments is obtained via technique of fixed-point theorems and analytic semigroup method. Finally, an example is given to explain the applicability of the abstract results developed.

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