ButtonFader.cs

using UnityEngine;
using System.Collections;
using UnityEngine.UI;

public class ButtonFader : MonoBehaviour {

    public bool faded = false;

    Image buttonImage;
    Text txt;
    Color buttonColor;
    Color textColor;
    bool startFade = false;
    float smooth = 0;
    bool initialized = false;

    void Start()
    {
        Initialize();
    }

    void Initialize()
    {
        startFade = false;
        faded = false;
        buttonImage = GetComponent<Image>();
        buttonColor = buttonImage.color;
        if (GetComponentInChildren<Text>())
        {
            txt = GetComponentInChildren<Text>();
            textColor = txt.color;
        }
        initialized = true;
    }

    void Update()
    {
        if (startFade)
        {
            Fade(smooth);
            if (buttonColor.a > 0.9)
                faded = true;
        }
    }

    public void Fade(float rate)
    {
        if (!initialized)
            Initialize();
        smooth = rate;
        startFade = true;
        buttonColor.a += rate;
        buttonImage = GetComponent<Image>();
        buttonImage.color = buttonColor;
        if (txt)
        {
            textColor.a += rate;
            txt.color = textColor;
        }
    }
}