L^p-solutions of fractional differential equations

Authors

T. A. Burton, Northwest Research Institute
Bo Zhang, Fayetteville State University

Document Type

Article

Publication Date

12-1-2012

Abstract

We study fractional differential equations of Caputo type cDqx(t)=u(t,x(t)), 0 < q < 1, of both linear and nonlinear type. That equation is inverted as an integral equation with kernel C(t-s):= (1/G(q))(t-s)q-1. We then transform the integral equation into one with kernel R(t-s) so that 0 < R(t) ?C(t) and ?0? R(s)ds = 1. A variety of techniques are introduced by which we are able to show that solutions are in L,p[0,?] for appropriate p ? 1. © CSP - Cambridge, UK; I&S - Florida, USA, 2012.

Recommended Citation

Burton, T. A. and Zhang, Bo, "L^p-solutions of fractional differential equations" (2012). College of Health, Science, and Technology. 859.
https://digitalcommons.uncfsu.edu/college_health_science_technology/859