For α∈(1,2), we analyze a stationary superdiffusion equation in the right angle in the unknown u=u(x1,x2): Dx1αu+Dx2αu=f(x1,x2), where Dxα is the Caputo fractional derivative. The classical solvability in the weighted fractional Hölder classes of the associated boundary problems is addressed.
In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.
<abstract><p>The solvability of some $ p $-Laplace boundary value problems with Caputo fractional derivative are discussed. By using the fixed-point theory and analysis techniques, some existence results of one or three non-negative solutions are obtained. Two examples showed that the conditions used in this paper are somewhat easy to check.</p></abstract>
Boundary-value problems for differential inclusions with Riemann–Liouville fractional derivative
