OpenGL Fragment Shader simulates the slow response time of the LCD screen

I have a very simple OpenGL view that renders 2 triangles with a single applied texture. The minimum configuration for rendering a 2D part.

What I do is redraw the texture for each image and easily get 60 frames per second.

I'd like to add an effect simulating a slow response from the LCD by generating pixels corresponding to the average between the current image and the previous image.

The pseudo fragment shader code would look like this

variant vec2 v_TexCoordinate;
uniform sampler2D u_Texture;

void main () {
gl_FragColor = (texture2D (u_Texture, v_TexCoordinate) + PIXEL_PREVIOUS_FRAME) / 2;

Well, I think that shaders can not keep a persistent variable like PIXEL_PREVIOUS_FRAME, so I really do not know how to fix this problem.

Any suggestion?