Type: Article

A new unified approach to study fractional PDE equations on a half-line

Kaikina, Elena I.;

Abstract:

We consider the initial-boundary value problem on a half-line for the evolution equation (partial derivative i + Sigma(n)(l) c(k)partial derivative(k)(x) + Sigma(m1)(l) b(k)partial derivative(beta k)(x) + Sigma(m2)(l) a(k)vertical bar partial derivative(x)vertical bar(ak)) with a fractional Abel type derivative vertical bar partial derivative(x)vertical bar(ak) u R1-ak+[ak]partial derivative x[ak]+l(u), and a fractional Caputo derivative partial derivative(beta k)(x) u=I1-beta k+[beta k]partial derivative x[beta k]+i(u), Here is the Riemann-Liouville fractional derivative. We study traditionally important problems of the theory of partial differential equations (PDEs), such as the existence and the uniqueness of the solution. We propose a new method for finding a solution. Also we get a closed form of the solution.