How to express dynamics when my problem comes from a PDE?

Sorry but I dont know how to insert my code. Many sign disappears. I will renew it if someone can tell this.
I am following a paper and want to repeat its result, but I get an infeasible status at the beginning. I want to know if I make some mistake in my code. Using one equality sign or two may be trouble I guess.
Thank you for your kindly advice.
The first problem is this:

My code is this:

cvx_begin
    variables T(3,N)  Gamma(N) kappa_aR(N)
    expressions m(N) r(3,N) v(3,N) a(3,N) a_R(3,N) 
    minimize(-w_mf*m(N)+w_kappaaR*norm(kappa_aR,2));
    %boundary conditions
    subject to
        m(1) == m_0;r(:,1) == r_0;v(:,1) = v_0;
        T(:,1) == Gamma_0vac.*n_0hat;Gamma(1) == Gamma_0vac;
        r(:,N) == [0,0,0]';v(:,N) == [0,0,0]';
        T(:,N) == Gamma(N).*n_fhat;
    %Dynamics    
    for i = 1:k_f
        m(i+1) = m(i)-(alpha/2*(Gamma(i)+Gamma(i+1))+dm_bp)*dtau;
        r(:,i+1) = r(:,i) + dtau.*v(:,i) +(dtau^2/3).*(a(:,i)+a(:,i+1)./2);
        v(:,i+1) = v(:,i) + (dtau/2).*(a(:,i)+a(:,i+1)); 
    end
    for i = 1:N
        a(:,i) = (T(:,i)-(rho*S_D*C_D*s(i)/2).*v(:,i))./mu(i)+a_R(:,i)+g;
    end
    %state constriants
    for i = 1:N
        m_dry<=m(i); 
        norm(r(:,i),2)*cos(gamma_gs)<=e_uhat'*r(:,i);
    end
    %control constriants
    for i = 1:N
        norm(T(:,i),2)<=Gamma(i);
        T_min<=Gamma(i)<=T_max; 
        Gamma(i)*cos(theta_max)<=e_uhat'*T(:,i);
    end
    for i = 1:k_f
        dT_min*dtau<=Gamma(i+1)-Gamma(i)<=dT_max*dtau;
    end
    %SC Modifications
    for i = 1:N
        norm(a_R(i),2)<=kappa_aR(i);
    end   
cvx_end

There is more than one way to do this in CVX. I suggest not using expressions with assignments, which use = . So,don’t have any declared expressions. Only use equality constraints, which are == . It should be straightforward to implement in CVX.

If you need more help,. please provide all input data, so that the problem is repoducible by forum readers.

Thanks so much for your advice. It works now.
It seems I made it too complicated at first.