Positive solutions for Hadamard-type fractional differential equations with nonlocal conditions on an infinite interval

The purpose of this paper is to analyse the local existence and uniqueness of positive solutions for a Hadamard-type fractional differential equation with nonlocal boundary conditions on an infinite interval. The technique used to arrive our results depends on two fixed point theorems of a sum operator in partial ordering Banach spaces. The local existence and uniqueness of positive solution is given, and we can make iterative sequences to approximate the unique positive solution. For the illustration of the main results, we list two concrete examples in the last section

Graphics processing unit accelerating compressed sensing photoacoustic computed tomography with total variation

Photoacoustic computed tomography with compressed sensing (CS-PACT) is a commonly used imaging strategy for sparse-sampling PACT. However, it is very time-consuming because of the iterative process involved in the image reconstruction. In this paper, we present a graphics processing unit (GPU)-based parallel computation framework for total-variation-based CS-PACT and adapted into a custom-made PACT system. Specifically, five compute-intensive operators are extracted from the iteration algorithm and are redesigned for parallel performance on a GPU. We achieved an image reconstruction speed 24–31 times faster than the CPU performance. We performed in vivo experiments on human hands to verify the feasibility of our developed method