This nine-chapter monograph introduces a rigorous investigationof "q-"difference operators in standard and fractional settings. It starts with elementary calculus of "q-"differences and integration of Jackson's type before turning to "q-"difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular "q-"Sturm-Liouville theory is also introduced; Green's function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of...