What is the exact condition for fractional integrals and derivatives of Besicovitch functions to have exact box dimension?

G.L. He and S.P. Zhou

Chaos, Solitons & Fractals, 2005, vol. 26, issue 3, 867-879

Abstract: Let 10 with λk→∞ satisfy the Hadamard condition λk+1/λk⩾λ>1. For a class of Besicovich functions B(t)=∑k=1∞λks-2sin(λkt), the present paper investigates the intrinsic relationship between box dimension of graphs of their vth fractional integrals g(t) and uth fractional derivatives g˜(t) and the asymptotic behavior of {λk}. We show that: if 01+v, then for sufficiently large λ, dim¯BΓ(g)=dim̲BΓ(g)=s-v holds if and only if limn→∞logλn+1logλn=1; if 0Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:26:y:2005:i:3:p:867-879

DOI: 10.1016/j.chaos.2005.01.041

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