Open AccessContinuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions
Author(s) -
Fatma M. Gaafar
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.12.008
Subject(s) - mathematics , fixed point theorem , uniqueness , nonlinear system , initial value problem , order (exchange) , schauder fixed point theorem , integrable system , picard–lindelöf theorem , cauchy distribution , mathematical analysis , physics , finance , quantum mechanics , economics
In this article, we discuss the existence of at least one solution as well as uniqueness for a nonlinear fractional differential equation with weighted initial data and nonlocal conditions. The existence of at least one L1 and continuous solution will be proved under the Carathèodory conditions via a classical fixed point theorem of Schauder. An example is also given to illustrate the efficiency of the main theorems