You make a vector of R1 with size 1x391 in the BANANA function. Thus you have a vector of 1x391 as result - one entry for every element of R1. Since you only provide only one initial time this leads to an error. To solve for many R1 the same time use an initial vector which provides as many elements as R1 has and transpose the result in BANANA:
t_zi = zeros(391,1);
zspan = [1*(10^-3) 0.0205];
[z,t] = ode45(@banana, zspan, t_zi);
plot(z,t);
hold off
title('Radius of banana vs Time')
xlabel('Radius of banana (µm)')
ylabel('t0 (min)')
function dtdz = banana(z,~)
%given conditions:
n = 1.23;
zi = 145*(10^-3);
z0 = 8.45;
u0 = 23*pi;
B0 = 0.0054;
h = 0.00734;
g = 10;
xs = 0;
xm = 0.00004386;
ps = 1937;
pm = 1.0995e+03;
c = 0.375;
T = 36;
%assume:
R1 = 10:400;
R = R1.*10^-6;
%initial conditions:
alpha = (8/9).*(((xs-xm).*B0.*R.^2)./(u0.*h.^2.*n));
beta = ((2.*R.^2)./(9.*n)).*(((ps-pm).*g-(2/h).*(((xs-xm).*B0.^2)/u0)));
dtdz = (1./(alpha.*z+beta))';
end
