I made this simple wing glider and put some ailerons on it. I thought that the ailerons in this glider would work the same way it works on airplanes, wherein the roll will be in the direction of the aileron that is pulled up. However, the opposite happens. For example, when I pull the left aileron up and the right aileron down, instead of rolling to the left, it rolls to the right. What is the reason behind this? And what is the difference between the control of this flying wing to a conventional airplane?
Most likely the adverse yaw effect (due to the induced drag of the increased lift on the down-aileron side) is causing the wing to yaw the opposite direction from the intended roll, and the yaw causes the dihedral induced roll (proverse to the yaw) to override the aileron input.
This situation is very commonly seen with very slow flying model aircraft -- indoor Peanut scale, for instance, or Penny Plane models, will often be set to turn left by putting a relatively tiny tab under the left wing, where you'd expect the lift to cause a roll to the right.
This opposite turn/bank effect predominates in very slow flight because the small differences in lift due to low deflections or small tabs are quite minor at low speed, while drag changes (especially with the relatively long moment arm of a drag tab on the outer section of the wing) are larger relative to other forces in play.
The general rule in trimming free flight models is that roll effects (from ailerons or tabs adding or subtracting life on one wing) will predominate at high speeds, while yaw effects (primarily produced by drag tab, as fin/rudder deflection is prone to produce a spiral dive) will predominate in slower flight. And extreme case is hand launch gliders, in which a single small tab under the left wing will cause the model to climb to the right (at the high speed -- up to 40 m/s or higher with a well-trained flier) due to the lift effects, but then glide to the left (at speeds as low as 4-5 m/s) due to drag effect of the same tab.
In some aircraft, such as the Canadair CP-107 Argus, the control yoke is not actually connected to the ailerons. Rather, they are connected to servo tabs, which are basically small ailerons attached to the rear of the actual ailerons (not to be confused with trim tabs, which look exactly the same but are controlled differently). Turning the yoke left causes the left servo tab to angle down, which deflects the actual aileron up. The aileron deflects the air stream upward, pushing the left wing down. The opposite happens on the right aileron and tab, raising that wing.
This effect can also occur unintentionally. For example, the Boeing B-47 Stratojet couldn't fly faster than 425 knots; above that speed, the ailerons would twist the wings so much that the airplane would roll in the opposite direction from what the pilot commanded.
I think it's likely that you're experiencing this. It's possible that the upward-turned aileron is twisting the whole wing downward enough that the plane rolls in the opposite direction from what you wanted. If that's the case, your options are to either stiffen the wings somehow, or just accept that your ailerons are going to work in the opposite way than you think they should.
can you elaborate why this (adverse yaw) is more common on slow flying aircraft
It may be a very good illustration of how Reynolds number can affect Lift to Drag ratios of airfoils and how Newtonian deflection of air by the bottom wing (downwash) helps drive low pressure creation (Coanda) on the upper wing only when velocity is sufficient.
Reynolds Number = wing chord m x Velocity m/s ÷ (1.46 x 10$^-5$)
Model aircraft can be faithfully scaled from full size because their density, or wing loading, is much lower. But, as @Zeiss Ikon pointed out, at lower speeds drag effect of a trim tab will predominate. This is consistent with L/D data presented at here at various Reynolds numbers. Small, slow models tend to be around 20,000, whereas full scale aircraft in the millions.
can it be solved with a larger vertical stabilizer?
This is exactly why rudder is used to counter-act adverse yaw. You make you vertical stabilizer "larger" by increasing its "sideways" coefficient of lift when you use coordinating rudder.
For a your free flight model, you can take advantage of the slow fight drag effect by not using ailerons. Just make a little rudder on the side of the wing tip fold you desire to turn into.
This is nothing radical at all. Using rudder yaw lets the dihedral roll the plane. This technique was common in 2 channel R/C aircraft years ago.