Your first function is messed up with code after the end that closes the function myObjective, try this change
function chisquare=myObjective(P,straindata,Timedata)
% expdata=load('ru.txt'); % Better to send in straindata
% straindata=expdata(:,2); % and Timedata as parameters than
% Timedata=expdata(:,1); % to load them every time you call the function
a = 0.5179;
b = 1.1003E-3;
c = 0.4576;
d = 1;
sigma = 180;
hstress = 3463.46;
Hstar = 0.7846;
Kc = 0.1137;
tspan = 0:0.01:40;
initial_conditions = [0;0;0;0];
function dy=pair1(t,y,a,b,d,hstress,sigma,Hstar,kc,c) % local function definition
dy=zeros(4,1);
dy(1) = a*sinh((b*(sigma^d)*(1-y(2)))/((1-y(3))*(1-y(4)))) ;
dy(2) = ((hstress*(a*sinh(b*(sigma^d)*(1-y(2)))/(1-y(3))*(1-y(4))))/(sigma^d))*(1-y(2)/Hstar);
dy(3) = (kc/3)*power((1-y(3)),4);
dy(4) = c*y(1);
end
% end % <- this end ends the function myObjective so everything after this line confuses matlab
[t,y] = ode45(@(t,y)pair(t,y,a,b,d,hstress,sigma,Hstar,Kc,c),tspan,initial_conditions) %function call
plot(t,y(:,1)) % while testing OK...
diffsquare(:,i) = ((expdata(i,2) - y(1)).^2)/n;
end
chisquare = sum(diffsquare);
global c; % Avoid globals like the plague -.even if this is for an acceptable cause put that comment in to discourage use
c = (chisquare);
Then you have to make minor modifications to your script as well:
% Here you load the data-file, now your Objective-function is applyable for multiple events and cases,
% this script file is what you copy-n-modify for different data-sets, much more reproducible and leaner
% work process.
expdata = load('ru.txt');
straindata = expdata(:,2);
Timedata = expdata(:,1);
P0 = [7E-6; 5E-6; 0.5; 0.43];
lb = [1E-6; 5E-8; 0; 0.42];
ub = [3E-5; 9E-6; 1; 0.5];
P = fmincon(@(P) myObjective(P,straindata,Timedata),P0,[],[],[],[],lb,ub);
plot(t,Straindata,'+-','Linewidth',1.5,'color','red');
hold on
plot(t,y(1),'--','Linewidth',1.5,'color','blue');
xlabel('Time');
ylabel('Strain');
Haven't checked anything but these changes you should do first.
HTH
