... transform. If we return back to Eq. 4 and apply the bilateral Laplace transform (LT), 10 G ( s ) = ∫ − ∞ + ∞ g ( t ) e − st dt to both sides ( 11 ). We conclude that 11 LT [ D f α g ( t ) ] = s α G ( s )     for   Re ( s...

... related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely, those based on the Taylor’s series and the Laplace transform...

... in finding the Laplace-domain solution of a fractional-order differential equation. differential equations Laplace transforms time-domain analysis gamma function fractional-order system initialization The incomplete gamma function and the (complete) gamma function occur regularly...

...Carl F. Lorenzo; Tom T. Hartley It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized...