Title Traveling wave with beta derivative spatialtemporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods Type Article Keywords Not Record Abstract Not Record Researchers M.F. Uddin (First researcher) , Golam Hafez (Second researcher) , Zakia Hammouch (Third researcher) , hadi rezazadeh (Fourth researcher) , Dumitru Baleanu (Fifth researcher)