Systems of Fractional Partial Differential Equations

In recent years, considerable interest in differential equations of fractional order has been caused by their numerous applications in many fields of science and technology. This circumstance served as an impetus for the development of the theory of boundary value problems for equations and systems of partial differential equations of fractional order, which has now become one of the intensively developing areas of modern mathematics.
We describe classes of well-posed initial and initial-boundary value problems for linear systems of partial differential equations of fractional order not exceeding one. We will show that these systems can be divided into two different types, which differ significantly in terms of setting correct boundary value problems. The first type includes systems with sign-definite eigenvalues of matrix coefficients in the main part. The second type includes systems of matrix coefficients in the main part of which have eigenvalues of different signs.