ploting Mitagg leffler function

Hello h

How can I plote the Mittage leffler for the function in [0,50], Here is the code but I do not know how to define the function.

I appreciate your help.

alpha=0.5;
beta=1.2;
function E= ML(z,alpha,beta)
plot(E)
end

Answer 1

[Sulaymon Eshkabilov]

Follow this approach. Let's say you'd need to plot: f(a, b, t) = a*exp(cos(b*t)) using a nested function.

a = 2.13;
b = 3.5;
t = linspace(-10, 10, 500);
OUTPUT=My_Fun(a, b, t);

function F = My_Fun(a, b, t)
F = a*exp(cos(b*t));
plot(t, F)
end

[Erm]

Thank you for help. But in the follwing code there is an error (Unrecognized function or variable 'E') , and I do not know how to fix it

alpha=0.2;
beta=0.3;
t = linspace(0, 1, 50);
z=-sqrt(t);
function E= ML(z,alpha,beta)
plot(E,t)
end 

[Torsten]

Yes, MATLAB's question is justified: You say you want to return "E" from your function "ML":

function E= ML(z,alpha,beta)

but you don't define it therein. You only write a senseless plot command:

plot(E,t)

[Sulaymon Eshkabilov]

What Torsten indicated is that you should define what is the formulation of E.

eg.,: E = alpha+beta*z

[Erm]

E is sum_{k=0}^{infty} z^k/Gamma(alpha*k+beta) and I wrote it as

syms k z alpha beta 
E=symsum(z^k/gamma(alpha*k+beta),k,0,Inf)

but still not working

[Walter Roberson]

alpha = sym(0.5);
beta = sym(1.2);
syms k z
E(z) = symsum(z^k/gamma(alpha*k+beta),k,0,Inf)

E(z) = 

t = linspace(-10, 10, 50).';

Y = E(sqrt(sym(t)))

Y = 

y = double(Y);
subplot(2,1,1); plot(t, real(y), 'k-.'); title('real part');
subplot(2,1,2); plot(t, imag(y), 'r:.'); title('imag part')

Answer 2

[Walter Roberson]

I suggest that you look in the File Exchange. I see at least 4 contributions for calculating Mittag Leffler function.

https://www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function

https://www.mathworks.com/matlabcentral/fileexchange/48154-the-mittag-leffler-function

https://www.mathworks.com/matlabcentral/fileexchange/64370-lrtfm-mittag-leffler-function

https://www.mathworks.com/matlabcentral/fileexchange/20849-generalized-mittag-leffler-function

Answer 3

[Sulaymon Eshkabilov]

As shown in one of the matlab exchange, edit this below shown function file using your own input variables, viz. k, z, alpha, beta

a = ?;
b = ?;
c = ?;
x = ?;
OUTPUT=ML_fun(a, b, c, x);

function f=ML_fun(a,b,c,x)
 gamma_c=1.0/gamma(c);
 f=0; fa=1; j=0;
 while norm(fa,1)>=eps
    fa=(gamma(c+j)*gamma_c)/gamma(j+1)/gamma(a*j+b) *x.^j;
    f=f+fa; j=j+1; 
    % You can also add: plot(), hold on % see the simulation progress of ML
    % fcn
 end
    % Or here: plot()
end