**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30850

##### Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition

**Abstract:**

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

**Keywords:**
Fractional diﬀerential equation,
Banach contraction principle,
Integral boundary condition,
Schauder fixed point theorem

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1335374

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