Linear differential systems with conditionally integrable coefficients

Completely Integrable Differential Systems Are Essentially Linear

Let ẋ = f(x) be a C autonomous differential system with k ∈ N ∪ {∞, ω} defined in an open subset Ω of R. Assume that the system ẋ = f(x) is C completely integrable, i.e. there exist n−1 functionally independent first integrals of class C with 2 ≤ r ≤ k. If the divergence of system ẋ = f(x) is non–identically zero, then any Jacobian multiplier is functionally independent of the n − 1 first integ...

Towards classification of conditionally integrable evolution systems

Given a generalized (Lie–Bäcklund) vector field, we classify (under certain nondegeneracy assumptions) all (1+1)-dimensional evolution systems which admit this vector field as a conditional symmetry. The connection with the theory of symmetries of systems of ODEs and with the theory of invariant modules is discussed.

On systems of linear fractional differential equations with constant coefficients

This paper deals with the study of linear systems of fractional differential equations such as the following system: 0096-3 doi:10 * Co E-m Y ða 1⁄4 AðxÞY þ BðxÞ; ð1Þ where Y ða is the Riemann–Liouville or the Caputo fractional derivative of order a (0 < a 5 1), and AðxÞ 1⁄4 a11ðxÞ a1nðxÞ . . . . . . . . . an1ðxÞ annðxÞ 0BBBBBB@ 1CCCCCCA; BðxÞ 1⁄4 b1ðxÞ . . . . . . . . . bnðxÞ 0BBBBBB@ 1CCCCCCA...

Higher-Order Linear Differential Systems with Truncated Coefficients

We consider the following problem: given a linear differential system with formal Laurent series coefficients, we want to decide whether the system has non-zero Laurent series solutions, and find all such solutions if they exist. Let us also assume we need only a given positive integer number l of initial terms of these series solutions. How many initial terms of the coefficients of the origina...

Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk)