Mild and strong solutions for a fractional nonlinear Neumann boundary value problem

Faculty Science Year: 2013
Type of Publication: Article Pages: 341-352
Authors:
Herzallah, Mohamed A. E, El-Shahed, Moustafa, Baleanu, Dumitru
Journal: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS EUDOXUS PRESS, LLC Volume: 15
Research Area: Computer Science; Mathematics ISSN ISI:000315700000015
Keywords : Fractional Caputo derivative, Boundary value problem, Neumann conditions, Schauffer fixed point theorem    
Abstract:
In this paper, we investigated the following fractional Neumann boundary value problem D-C(0)alpha+u(t) - lambda u(t) = f (t, u(t)), u'(0) = u'(1) = 0, 1 < alpha < 2, lambda not equal 0, where D-C(a+)alpha is the fractional Caputo derivative. We proved the existence of at least one mild solution and we determined when this solution is unique for suitable assumptions on the function f
    
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