(c1)-solution (c2)-solution Caputo derivatives Optimal Auxiliary Functions Method Riccati transformation Sonine kernel adsorption approximate solution asymptotic regularity chaos commensurate order comparison theorem complexity control delays controllability convolution series damping term diffusion discrete SIR epidemic model discrete fractional calculus discrete nabla Riemann–Liouville fractional differences distributed deviating arguments dynamics impact elastic collision fading memory finite element fourth-order fractional behaviours fractional calculus fractional derivative