$form['activity']['submit'] = array(
      '#type' => 'button',
      '#value' => t('Execute'),
      '#name' => 'test_button',
      '#submit' => array('my_custom_form_submit')
    );

$form['activity']['submit'] = array(
  '#type' => 'button',
  '#value' => t('Execute'),
  '#name' => 'test_button',
  '#ajax' => array(
    'callback' => '_handle_form_submit',
    'effect' => 'fade',
),
);

 function _handle_form_submit($form, $form_state) {
 // your stuff here
 }