Soft Numerical Computing in Uncertain Dynamic Systems

$x_l\left(t,r\right)=r\left(1-sinht\right)+sinht-cost$

$x_u\left(t,r\right)=\left(2-r\right)\left(1-sinht\right)+sinht-cost$

wIf we consider the derivatives of the solution, it is ii − gH differentiable and in level-wise form there is interchanging of the end points of the interval and it looks like Fig. 4.16, but the lower and upper functions are changed. In addition, it happens for the x′′, and this means x′ is ii − gH differentiable too. Therefore, the solution is not acceptable.

Case IV. Both functions x, x′ are ii − gH differentiable.

Then by taking the Laplace transform and:

$\left(-1\right)\odot {\sigma }_0\oplus s^2\odot L\left(x\left(t\right)\right){\ominus }_{H}s\odot {\sigma }_0\oplus L\left(x\left(t\right)\right)=\frac{{\sigma }_0}{s}$

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