@acer 

if I want to change the parameter to lambda=0.01..1, and a = 0.0..1.0, how to run that code in maple for nonlinearfit?

@acer parameters lambda range from 0 to 0.1, and alpha from 0 to 2, it came from the fractional differential equation of exponential function, thanks.

@acer 

Thank you very much, it helped me in my work. Right, the alpha and lambda parameters are in a range, the results are acceptable for me, and I got a new approximation of the Y variable. Thank you again.

@acer 

thanks for the answer, I tried to correct it as mentioned by you, but this is the result

Download WB_Fractional_Derivative.mwWB_Fractional_Derivative.mw

ExpFDE4 := Y(1)*(Sum(lambda^k*t^(k*a)/factorial(k*a), k = 0 .. infinity))

t := 't'

Statistics[NonlinearFit](ExpFDE4, X, Y, t)

Error, (in Statistics:-NonlinearFit) could not store 690.3687744*(Sum(HFloat(0.0), HFloat(1.0) = 0 .. infinity))-HFloat(690.3687744) in a floating-point rtable