I would appreciate help with this task:
Solve the following system of fractional differential equations:
$$ \begin{cases}A_{1} \cdot D^{2}_{t}y(t)+A_{2} \cdot D^{1}_{t}y(t)+A_{3} \cdot y(t) = 1 \\ B_{1} \cdot D^{2}_{t}y(t)+B_{2} \cdot D^{1}_{t}y(t)+B_{3} \cdot y(t) + B_{4} \cdot D^{v}_{t}y(t) = B_{5} + B_{6} \cdot \frac{t^{-v}}{\Gamma(-v+1)} \end{cases} $$ where $ A_{1},A_{2},A_{3},B_{1},B_{2},B_{3},B_{4},B_{5},B_{6} $ are known real numbers
and $ v $ is known real positive number $ (v>0) $
(actually, only the second equation is fractional)
We also know that $y(0)=0$
I want to write a program in Matlab which will find the $y(t)$ , given $A_{1},A_{2},A_{3},B_{1},B_{2},B_{3},B_{4},B_{5},B_{6}$ and $v$
It is okay to use external scripts.
Update: Thank you for your comments. I have edited the formatting according to them.
Yes, a numerical solution would be good enough. Yes, I have found scripts for Matlab to solve fractional differential equations:
However, they need the set of initial conditions, which are not given in this task.
$D^{\alpha}_{x}$ is a fractional differintegral. For $\alpha > 0$ it is a fractional derivative: http://mathworld.wolfram.com/FractionalDerivative.html
Update 2: I've replaced $-v$ with $v$ and corrected $\gamma$ to $\Gamma$
Update 3: Now the task is easier. We know that $y(0)=0$