Existence and uniqueness of solution for some class of nonlinear fractional order differential equations
نویسنده
چکیده
Abstract: In this article, we discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations ( Dα − ρtDβ ) x(t) = f (t, x(t), Dγx(t)) , t ∈ (0, 1) with boundary conditions x(0) = x0, x(1) = x1 or satisfying the initial conditions x(0) = 0, x′(0) = 1 where D denotes Caputo fractional derivative, ρ is constant, 1 < α < 2 and 0 < β + γ ≤ 1. Schaurder’s fixed point Theorem is the main tool used here to establish the existence. We use Banach contraction principle to show the uniqueness of the solution under certain conditions on f .
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