Problem with Nonlinear Least Squares fitting

I am trying to create a script that will fit some scientific data to the function

where a,b, and c are the fitting parameters. My problem is that the script does not seem to seek better parameters, but I can do the fitting in a different software. What is wrong with my code? My code is below, and I am very new to MatLab. Thank you.

x = A(389:401, 6);
y = A(389:401, 5);
axis([0 1010 0 1.6E-7])
% hold on
plot(x,y,'ro')
title('Data points')
% hold off

ft = fittype('(a/2)*(sin(b*pi/2)/(cosh(b*log(2*pi*x*c))+cos(b*pi/2)));');
fo = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[-1,-1,-1],...
               'Upper',[1,1,1],...
               'StartPoint',[5e-7 0.63 9e-5]);
[f2,gof,output]=fit(x,y,ft,fo);
f2
gof.rsquare
figure
plot(f2,x,y)

Answer 1

[Sam Chak]

@Jason Yee

I don't see anything technically wrong with code. Probably the choices of the lower and upper bounds are 'too vast'. Your data lies in this region?

axis([0 1010 0 1.6E-7])

Does your data look like these two curves?

x = linspace(-pi, pi, 3601);
y1 = (1/2)*(sin(1*pi/2)./(cosh(1*log(2*pi*x*1))+cos(1*pi/2)));
y2 = (-1/2)*(sin(-1*pi/2)./(cosh(-1*log(2*pi*x*-1))+cos(-1*pi/2)));
plot(x, [y1' y2'])

[Jason Yee]

Hello

I tried narrowing the constraints on my starting values.

ft = fittype('(a/2)*(sin(b*pi/2)/(cosh(b*log(2*pi*x*c))+cos(b*pi/2)));');
fo = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[0,0,0],...
               'Upper',[1e-6,1,1e-4],...
               'StartPoint',[5.4e-7 0.67 9e-5]);
[f2,gof,output]=fit(x,y,ft,fo);
f2
gof.rsquare
figure
plot(f2,x,y)

Do you recommend the lsqcurvefit function? Thank you.