Bikash Gogoi | Searcharxiv

arXiv2022

Impulsive Fractional Dynamic Equation with Non-local Initial Condition on Time Scales

In this manuscript we investigate the existence and uniqueness of an impulsive fractional dynamic equation on time scales involving non-local initial condition with help of Caputo nabla derivative. The existency is based on the Scheafer's fixed point theorem along with the Arzela-Ascoli theorem and Banach contraction theorem. The comparison of the Caputo nabla derivative and Riemann-Liouvile nabla derivative of fractional order are also discussed in the context of time scale.

math.AP↗

arXiv2021

Nabla Fractional Derivative and Fractional Integral on Time Scales

In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Grünwald-Letnikov sense. Some of the basic properties and theorems related to nabla fractional calculus are discussed.

math.GM↗

arXiv2019

Custom Code Generation for a Graph DSL

Graph algorithms are at the heart of several applications, and achieving high performance with them has become critical due to the tremendous growth of irregular data. However, irregular algorithms are quite challenging to parallelize automatically, due to access patterns influenced by the input graph, which is unavailable until execution. Former research has addressed this issue by designing domain-specific languages (DSLs) for graph algorithms, which restrict generality but allow efficient code-generation for various backends. Such DSLs are, however, too rigid, and do not adapt to changes in backends or to input graph properties or to both. We narrate our experiences in making an existing DSL, named Falcon, adaptive. The biggest challenge in the process is to not change the DSL code for specifying the algorithm. We illustrate the effectiveness of our proposal by auto-generating codes for vertex-based versus edge-based graph processing, synchronous versus asynchronous execution, and CPU versus GPU backends from the same specification.

cs.PL↗