Abstract
In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation where denotes the Caputo fractional differential operator of order α, 2 < α ≤ 3. A new result on the existence of solutions for above fractional boundary value problem is obtained. Mathematics Subject Classification (2000): 34A08, 34B15.
Highlights
1 Introduction Fractional calculus is a generalization of ordinary differentiation and integration on an arbitrary order that can be noninteger
As is known to all, the problem for fractional derivative was originally raised by Leibniz in a letter, dated September 30, 1695
The fractional derivative has been occurring in many physical applications such as a non-Markovian diffusion process with memory [1], charge transport in amorphous semiconductors [2], propagations of mechanical waves in viscoelastic media [3], etc
Summary
Fractional calculus is a generalization of ordinary differentiation and integration on an arbitrary order that can be noninteger. By using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation Dα0+ x(t) = f (t, x(t), x (t), x (t)), t ∈ [0, 1], x(0) = x(1), x (0) = x (0) = 0, where Dα0+ denotes the Caputo fractional differential operator of order a, 2
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