84 research outputs found
Terminal value problem for differential equations with Hilfer–Katugampola fractional derivative
We present in this work the existence results and uniqueness of solutions for a
class of boundary value problems of terminal type for fractional differential equations with the
Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of
classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point
theorem. We illustrate our main findings, with a particular case example included to show the
applicability of our outcomesThe research of J.J. Nieto was partially supported by the AEI of Spain under Grant MTM2016-75140-P and co-financed by the European Community fund FEDERS
Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
In this paper we obtain new estimates of the Hadamard fractional derivatives
of a function at its extreme points. The extremum principle is then applied to
show that the initial-boundary-value problem for linear and nonlinear
time-fractional diffusion equations possesses at most one classical solution
and this solution depends continuously on the initial and boundary conditions.
The extremum principle for an elliptic equation with a fractional Hadamard
derivative is also proved
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