Abstract :
A class of nonlinear fractional order partial differential equations with delay
c∂αu(x, t)
∂tα
= a(t)△u(x, t) + f (t, u(x, τ1(t)), . . . , u(x, τl(t))), t ∈ [0, T0]
be investigated in this paper, where cDα is the standard Caputo’s fractional derivative
of order 0 ≤ α ≤ 1, and l is a positive integer number, the function f is defined as
f (t, u1, . . . , ul) : R×R×· · · ,×R → R, and x ∈ 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.
Keywords :
Fractional order , Partial differential equations , Solution , Existence , Uniqueness , Delay