abiodunowoyemi9

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These are questions asked by abiodunowoyemi9

I have been having problem in solving this question because of the 'Whittaker'.

Can anyone please asist me how to integrate below problem with the 'Whitaker?

f := exp(-1.5*t)*(GAMMA(2)*t^(2-alpha)/GAMMA(3-alpha)-t^(1-alpha)/GAMMA(2-alpha)+t^2-t);
               /   (2 - alpha)        (1 - alpha)           \
               |  t                  t                 2    |
   exp(-1.5 t) |---------------- - ---------------- + t  - t|
               \GAMMA(3 - alpha)   GAMMA(2 - alpha)         /
int(f, t);
 

2.^(3.-1.*alpha)*3.^(alpha-3.)*(t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(alpha-3.)*(-2.+alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha, -.5000000000*alpha+.5000000000, 1.500000000*t)/(3.-1.*alpha)+t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(1.500000000*t-1.*alpha+2.)*(alpha-3.)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha+1., -.5000000000*alpha+.5000000000, 1.500000000*t)/(3.-1.*alpha))/GAMMA(3.-1.*alpha)-1.*2.^(2.-1.*alpha)*3.^(-2.+alpha)*(t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha, -.5000000000*alpha+.5000000000, 1.500000000*t)+t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(-2.+alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha+1., -.5000000000*alpha+.5000000000, 1.500000000*t)/(2.-1.*alpha))/GAMMA(2.-1.*alpha)+.1481481481+(0.9876543210e-1*(-6.750000000*t^2-9.*t-6.))*exp(-1.500000000*t)-(.2222222222*(-2.-3.*t))*exp(-1.500000000*t)

Please, is there anyway I can solve below problem without replacing the Alpha with value? The error I got is "Error, (in fracdiff) Unable to determine ceiling of alpha"

>

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>-fracdiff(U1, t, alpha)+U1/M-U1^2/(M*K)+diff(U1, t)-(diff(U1, t))/epsilon

>int(%, t)

Hi everyone,
Please I need your help, if anyone has idea of using Perturbation Theory to Solve the following Logistic Fractional Equation and ploting with iteration. Thanks

Restart

u(t):=1/(m)(u(t)-(u^(2)(t))/(k));

NULL

uu(t):=(k*u_0)/((u_0+(u_0)*k)*(e)^(-t/(m)))

NULL

u(0) = u_0

NULL

Please, is there anyway I can solve this problem with a nice output? The solution I got is complicated. Please, helper is need

f := exp(-beta*x)*x^(5-alpha)

int(f, x)

beta^(alpha-6)*(-x^(-alpha)*beta^(-alpha)*(alpha^4-14*alpha^3+71*alpha^2-154*alpha+120)*(alpha-6)*(beta*x)^((1/2)*alpha)*exp(-(1/2)*beta*x)*WhittakerM(-(1/2)*alpha, -(1/2)*alpha+1/2, beta*x)/(-alpha+6)+x^(-alpha)*beta^(-alpha)*(beta^4*x^4-alpha*beta^3*x^3+alpha^2*beta^2*x^2+5*beta^3*x^3-alpha^3*beta*x-9*alpha*beta^2*x^2+alpha^4+12*alpha^2*beta*x+20*beta^2*x^2-14*alpha^3-47*alpha*beta*x+71*alpha^2+60*beta*x-154*alpha+120)*(alpha-6)*(beta*x)^((1/2)*alpha)*exp(-(1/2)*beta*x)*WhittakerM(-(1/2)*alpha+1, -(1/2)*alpha+1/2, beta*x)/(-alpha+6))

Good day,
 

1. Please I need your greatest help. Can anyone please help me to run the examples on the attached papers on Maple software?

 2. Also help me to plot the graphs along with the exact solution

 3. If possible with tables

 I tried but did not get the results as expected. I shall be very grateful if I can get assistance from you

 

Thanks