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Extra resources for Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach
From the above example, x (1) doesn’t exist but R L derivative exists at t = 1. 25) x(t) = 0 if t = 1 ⎪ ⎩ 2 − t if 1 < t < 2. Then, if 0 < α < 1, we get ⎧ ⎪ ⎪ ⎨ t 1−α if 0 < t < 1 Γ (2 − α) RL α D x(t) = t 0 t 1−α − 2(t − 1)1−α ⎪ ⎪ ⎩ if 1 < t < 2. Γ (2 − α) Therefore, lim t = 1. 26) 1 R α Γ (2−α) . Then 0 L Dt x(t) exists at Example Riemann-Liouville derivative of the Weierstrass function (continuous everywhere but differentiable nowhere in classical sense) as shown in Fig. 8. One form of Weierstrass function is as follows  λ−μj sin(λ j t), (0 < μ < 1, λ > 1).
25) x(t) = 0 if t = 1 ⎪ ⎩ 2 − t if 1 < t < 2. Then, if 0 < α < 1, we get ⎧ ⎪ ⎪ ⎨ t 1−α if 0 < t < 1 Γ (2 − α) RL α D x(t) = t 0 t 1−α − 2(t − 1)1−α ⎪ ⎪ ⎩ if 1 < t < 2. Γ (2 − α) Therefore, lim t = 1. 26) 1 R α Γ (2−α) . Then 0 L Dt x(t) exists at Example Riemann-Liouville derivative of the Weierstrass function (continuous everywhere but differentiable nowhere in classical sense) as shown in Fig. 8. One form of Weierstrass function is as follows  λ−μj sin(λ j t), (0 < μ < 1, λ > 1). 3 Why Fractional Order?
After looking into the literature towards we are able to find one important work which is presented by Blas M. Vinagre and YangQuan Chen , 41st IEEE CDC-2002 tutorial workshop. This gives lots of motivation to us, to work and try to bring more researchers, academicians and industrial people towards this area, particularly fractional order system in the science and control engineering disciple. Before moving towards fractional order modeling and control a lot of restrictions of classical calculus is pointed out by Blas M.