It is not hard if you understand 1) how to write a good paint() method,
2) how to use threads.
Totally UNTESTED sorry!- but should give you a clue as to how to do it.

PS and you should also make these 3 bits synchronized: 1) relevant
section in the MyPanel.paint method, 2)makeBang, and 3) the call to
currentFragments.remove().

PPS if you are going to have lots of explosions at a time, you will be
better of making makeBang create multiple Timers rather than multiple
Threads. Same logic applies of course.

class MyPanel extends JPanel{
// a fragment stores the information for one piece
class Fragment{
 int x, y, vx, vy, alpha=0;
 Image i;
 public Fragment(int initx, int inity, Image image){
  /* set up pos and velocities */
 }
 public void paint(Graphics2D g){
  Composite oldComposite = g.getComposite();
  g.setComposite(AlphaComposite.getInstance(
     AlphaComposite.SRC_OVER, alpha/10f);
  g.drawImage(i,x,y,null);
  g.setComposite(oldComposite);
 }
 public void update(Graphics g){
  x=x+vx; y=y+vy; alpha++;
 }
}

// each element is an array of fragments representing one explosion
Vector currentFragments = new Vector();

// add an array of fragments to currentFragments, and
// set up a thread running a RunBang to process this.
void makeBang(int x, int y, Image i, int maxFragments){
 Fragment[] f = new Fragment[(int)(Math.random()*maxFragments)];
 for(int i=0;i<f.length;i++) f[i]=new Fragment(x,y,i);
 currentFragments.add(f);
 new Thread(new RunBang(f)).start();
}

// Repeatedly calls Fragment.update() on each fragment
// and repaint() to paint the panel again
class RunBang implements Runnable{
 Fragment[] fragment;
 public RunBang(Fragment[] f){ fragment=f; }
 public void run(){
  for(int i=0;i<10;i++){
   for(int j=0;j<fragment.length;j++){
    fragment[j].update();
   }
   repaint();
   try{Thread.sleep(200);}
   catch(InterruptedException e){e.printStackTrace();}
  }
  currentFragments.remove(f);
 }
}

// standard method to paint your stuff
// and any current explosions.
public void paint(Graphics g){
  /* draw the main part of your game etc. here */
  // then:
  // paint each of the current explosions
  Graphics2D g2 = (Graphics2D) g;
  for(int i=0;i<currentFragments.size();i++){
   Fragment[] fragments=(Fragment[])currentFragments.get(i);
   for(int j=0;j<fragments.length;j++) fragments[j].paintMe(g2);
  }
}
}