On Fractional and Fractal Derivatives in Relation to the Physics of Fractals

Authors

  • Roberto N. Padua
  • Miraluna L. Herrera Caraga State University
  • Adriano V. Patac Jr. Surigao State College of Technology
  • Michael V. Sabugaa Agusan del Sur State College of Agriculture and Technology
  • Gibson T. Maglasang Cebu Normal University
  • Mark S. Borres University of San Jose-Recoletos
  • Jay M. Ontolan Cebu Normal University

DOI:

https://doi.org/10.32871/rmrj1301.02.24

Keywords:

fractional derivative, fractal derivative, fractional differential operators, fractal analysis

Abstract

Fractional and fractal derivatives are both generalizations of the usual derivatives that consider derivatives of non-integer orders. Interest in these generalizations has been triggered by a resurgence of clamor to develop a mathematical tool to describe “roughness†in the spirit of Mandelbrot’s (1967) fractal geometry. Fractional derivatives take the analytic approach towards developing a rational order derivative while fractal derivatives follow a more concrete, albeit geometric approach to the same end. Since both approaches alleged to extend whole derivatives to rational derivatives, it is not surprising that confusion will arise over which generalization to use in practice. This paper attempts to highlight the connection between the various generalizations to fractional and fractal derivatives with the end-in-view of making these concepts useful in various physics applications and to resolve some of the confusion that
arise out of the fundamental philosophical differences in the derivation of fractional derivatives (non-local concept) and fractal derivatives (local concept).

Author Biographies

Roberto N. Padua

Dr. Roberto Natividad Padua, scientist, received his PhD in Mathematical Statistics from Clemson University, South Carolina, USA under the Fullbright-Hays scholarship grant. He is an accomplished author, a multi-awarded researcher and an internationally acclaimed lecturer. Dr. Padua is a former Commissioner of CHED and currently a consultant to several state and private universities. He is also conducting lectures on research and Fractal Statistics. Dr. Padua is a Summa Cum Laude, BS in Mathematics Teaching graduate from the Philippine Normal College under the National Science Development Board (NSDB) program. He obtained his MS in Mathematics Education Degree from the Centro Escolar University as a Presidential Scholar.

Gibson T. Maglasang, Cebu Normal University

is currently Instructor I at the Department of Chem-Physics of Cebu Normal University, Cebu City, Philippines. He completed his degree in Physics, in 2009 at the Mindanao State University – Iligan Institute of Technology and was awarded as Cum Laude. He obtained his MS Physics, in 2011 at the same university. The author has been an active member of the Samahang Pisika ng Visayas at Mindanao and has participated and presented various studies in SPVM national conference and workshop from 2008-2012 relating to theoretical and mathematical physics research topics. His areas of interest include mathematical and theoretical physics, quantum physics, biophysics, astrophysics, and computational physics.

Mark S. Borres, University of San Jose-Recoletos

graduated Bachelor of Science in Mathematics–major in Pure Mathematics at the University of the Philippines, Cebu College. Since 2009, he worked for the University of San Jose- Recoletos as a faculty member of the College of Arts and Sciences and handled Mathematics subjects such as College Algebra, Advanced Algebra, Abstract Algebra, Analytical Geometry, Euclidean geometry, Trigonometry, Business Mathematics, Linear Programming, Mathematics of Investment, Discrete Structure, and Statistics across colleges.

References

Anatoly N. Kochubei (2013) “Fractional-hyperbolic systems” (Journal of Fractional Calculus and Applied Analysis, Vol. 12)

Danijela Rajter-Ćirić, Mirjana Stojanović (2013) Fractional derivatives of multidimensional Colombeau generalized stochastic processes(Journal of
Fractional Calculus and Applied Analysis, Vol. 12)

Fourier. J. (1955) The Analytical Theory of Heat, Dover Publications, New York.

Padua, Roberto ; Palompon, Daisy; Ontoy, Dexter S. “Data Roughness and Fractal Statistics” (CNU-Journal of Higher Education, Vol. 7., No.2, 2013)

Pant, Lalit M.; Sushanta K. Mitra, Marc Secanell (2012). “Absolute permeability and Knudsen diffusivity measurements in PEMFC gas diffusion layers and micro porous layers”. (Journal of Power Sources, Vol. No. 20.)

Sabrina Roscani, Eduardo Santillan Marcus (2013). “ Two equivalent Stefan’s problems for the time fractional diffusion equation” (Journal of Fractional Calculus and Applied Analysis, Vol. 12)

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Published

2013-12-31

How to Cite

Padua, R. N., Herrera, M. L., Patac Jr., A. V., Sabugaa, M. V., Maglasang, G. T., Borres, M. S., & Ontolan, J. M. (2013). On Fractional and Fractal Derivatives in Relation to the Physics of Fractals. Recoletos Multidisciplinary Research Journal, 1(2). https://doi.org/10.32871/rmrj1301.02.24

Issue

Vol. 1 No. 2 (2013)

Section

Articles

License

Copyright of the Journal belongs to the University of San Jose-Recoletos