Existence and uniqueness of the solutions for a class of nonlinear fractional order partial differential equations with delay

Authors:
Zigen Ouyang
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
Cited 0

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Abstract

A class of nonlinear fractional order partial differential equations with delay ^c@?^@au(x,t)@?t^@a=a(t)@?u(x,t)+f(t,u(x,@t"1(t)),...,u(x,@t"l(t))),t@?[0,T"0] be investigated in this paper, where ^cD^@a is the standard Caputo's fractional derivative of order 0@?@a@?1, and l is a positive integer number, the function f is defined as f(t,u"1,...,u"l):RxRx...,xR-R, and x@?@W is a M dimension space. Using Lebesgue dominated convergence theorem, Leray-Schauder fixed point theorem and Banach contraction mapping theorem, we obtain some sufficient conditions for the existence of the solutions of the above fractional order partial differential equations.