Fractional Differential Equation
المؤلف:
Kilbas, A. A.; Srivastava, H. M.; and Trujiilo, J. J
المصدر:
Theory and Applications of Fractional Differential Equations. Amsterdam, Netherlands: Elsevier, 2006.
الجزء والصفحة:
...
12-6-2018
1413
Fractional Differential Equation
The solution to the differential equation
![[D^(2v)+alphaD^v+betaD^0]y(t)=0](http://mathworld.wolfram.com/images/equations/FractionalDifferentialEquation/NumberedEquation1.gif) |
(1)
|
is
![y(t)=<span style=]() {e_alpha(t)-e_beta(t) for alpha!=beta; te^(alphat)sum_(k=-(q-1))^(q-1)alpha^k(q-|k|)D^(1-(k+1)v)(te^(alpha^qt)) for alpha=beta!=0; (t^(2nu-1))/(Gamma(2v)) for alpha=beta=0, " src="http://mathworld.wolfram.com/images/equations/FractionalDifferentialEquation/NumberedEquation2.gif" style="height:122px; width:372px" /> |
(2)
|
where
is the Et-function, and 
is the gamma function.
REFERENCES:
Kilbas, A. A.; Srivastava, H. M.; and Trujiilo, J. J. Theory and Applications of Fractional Differential Equations. Amsterdam, Netherlands: Elsevier, 2006.
Miller, K. S. "Derivatives of Noninteger Order." Math. Mag. 68, 183-192, 1995.
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