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The interesting problems from fractional calculus and fractals are reported. With the scaling law, the scaling-law vector calculus via scaling-law calculus is suggested in detail. Some special functions related to the classical, fractional, and power-law calculus are also presented to express the Kohlrausch\u2013Williams\u2013Watts function, Mittag-Leffler function and Weierstrass\u2013Mandelbrot function. They have a relation to the ODEs, PDEs, fractional ODEs and fractional PDEs in real-world problems. Theory of the scaling-law series via Kohlrausch\u2013Williams\u2013Watts function is suggested to handle real-world problems. The hypothesis for the tempered Xi function is proposed as the Fractals Challenge, which is a new challenge in the field of mathematics. 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