Your ode appears to be stiff - therefore i recommend to use ode15s instead of ode45. Also the behaviour of your system can be seen much better with t=[0 0.01] instead of t=[0 1]. Note that there are several constants that are unused in your code. You see that these values are underlined in orange by Matlab inside the editor window.
However - here's a working code:
[t,y] = solveODE;
subplot(3,1,1)
plot(t,y(:,1))
subplot(3,1,2)
plot(t,y(:,2))
subplot(3,1,3)
plot(t,y(:,3))
function [t,y] = solveODE
%% Constants
T0=300;
mili=1e-3;
P=90*mili;
Pc=20*mili;
R1=24;%k/w
R2=7;
R3=9.4;
micro=1e-6;
lA=300*micro;
wA=1.2*micro;
tA=0.15*micro;%tickness
vA=lA*wA*tA;%volume
aA=lA*wA;%area
%pc structure
lP=250*micro;
wP=1.5*micro;
tP=0.25*micro;%tickness
vP=lP*wP*tP;
aP=lP*wP;%area
%Bragg section
lB=300*micro;
leff=135*micro;
wB=1.5*micro;
tB=0.25*micro;%tickness
vB=lB*wB*tB;
aB=lB*wB;
nm=1e-9;
RHOv=4.825e3;
V=[vA,vP,vB,vA,vP,vB];
Cv=3.124e2;
Cc=2.46e-7;
Cs=5.32e-5;
Cj=Cv*RHOv.*V;
C=mean(Cj);
m11=-1/(R2*Cc);
m12=-m11;
m13=1/(Cc*R1);
m21=1/(R2*Cs);
m22=-(1/R2+1/R3)*(1/Cs);
m23=0;
m31=6/(R2*Cc);
m32=-m31;
m33=-1/(R1*C)-6/(Cc*R1);
U1=Pc/Cc;
U2=T0/(R3*Cs);
U3=P/C-(6*Pc)/Cc;
%% solve the system
tspan=[0 0.01];
y0=[300 300 0];
[t,y] = ode15s(@odefcn,tspan,y0);
%% ODE function
function dydt = odefcn(~,y)
dydt=zeros(3,1);
dydt(1)= m11*y(1)+ m12*y(2)+ m13*y(3)+U1;
dydt(2)= m21*y(1)+ m22*y(2)+ m23*y(3)+ U2;
dydt(3)= m31*y(1)+ m32*y(2)+ m33*y(3)+ U3;
end
end
