Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 19, Issue 2, Pages 243-247Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X11005294
Keywords
Fractional Calculus; Fractional Derivatives; Fractional Variational Principle
Funding
- Department of Mechanical Engineering and Energy Processes (MEEP)
- Southern Illinois University-Carbondale, IL, USA
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In this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, by applying the variational principle to this new fractional action, we obtained the modified Euler-Lagrange equations of motion in any fractional time of order 0 < alpha <= 1. Two examples are investigated in detail.
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