Construction of Functions for Fractional Derivatives using Matlab
Journal of Advances in Mathematics and Computer Science,
MATLAB is a high level programming tool for technical computing, its application cuts across different sphere of science, engineering, finance, communication, music etc. With the current increase in the use of non-integer order derivatives, there is a need to have tools that handle them for effective applications. In this paper, we present a brief comparative review of 2 expressions of fractional derivative. MATLAB functions for approximating Riemann-Liouville and Caputo fractional derivatives are presented alongside. Numerical simulations with test examples are implemented and results compared. To effectively handle non-polynomial function, Taylor series expansion is employed to convert the function into a form that can be easily handled.
- fractional derivative
- caputo derivative
- riemann liouville derivative
How to Cite
Retrieved Jan 15, 2021.
Dean G Duffy. Advanced Engineering Mathematics with MATLAB, Taylor & Francis Group, CRC Press; 2017.
Bagley RL, Torvik PJ. A Theoretical basis for the application of fractional calculus to viscoelasticity J of Rheology. 1993;27:201-210.
Bagley RL, Torvik PJ. Fractional calculus, a differential approach to the analysis of viscoelastic ally damped structures. AIAA J. 1983;21(5):741-748.
Rosin DA. The use of control systems analysis in neurophysiology of eye movements. Ann. Rev Neurosci. 1981;4:462-503.
Magin RL. Fractional calculus in bioengineering. Critical Rev. Biomed. Eng. 2004;32:1-100.
Hilfer R. Application of fractional calculus in physics, World scientific, River Edge, N J, USA; 2000.
Sun HG, Chen N, Li CP, Chen YQ. Fractional differential models for anomalous diffusion, Physical. 2010;389(14):2719-2724.
Lakshmikantham V, Leela S. and Vasundhara J. Devi, “Theory of Fractional Dynamic Systems,” Camb. Acad. Publ., Cambridge, 2009.
Geoffrey B. West, James H. Brown and Brain J. Enquist, A general model for the origin of allometric scaling laws in biology, Science 276, 122; 1997.
Arqub OA. Numerical solutions for the Robin time fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm. J. Numer. Methods Heat Fluid Flow Int.
Anastasia G, Gavriil S, Al Khawaja U, Lincoln D. Carr, Expansion of fractional derivative in terms of an integral derivatives series: physical and numerical applications, arXiv preprint arXiv. 2017;1710.06297.
Gavriil S, Nathanael CS, Anastasia G, Lincoln D. Carr, Exact results for a fractional derivative of elementary functions. arXiv Preprint arXiv: 2017;1711.07126 .
Gavriil S, Nathanael CS, Anastasia G, Lincoln D. Carr, Fractional derivative of composite functions: exact results and physical applications. arXiv: 1803.05018v2 [math. CA] ; 2019.
Kamlesh Kumar, Rajesh k Pandey, Shiva Sharma. Approximations of fractional integrals and carpito derivatives with application in solving Asels integral equations J. of king Sand University-Service. 2019;31:692-700.
Ross B. Fractional calculus: An historical apologia for the development of non-integer orders, Mathematics Magazine. 1977;50(3):115-122.
Podlubny I. Fractional Differential Equations, Academic Press, San Diego; 1999.
Li C, Sarwar S. Existence and continuation of solution for capitol type fractional differential equations. Electron. J. Differ. Equation. 2016;1-4.
Arakaparampil M Mattai, Ram Kishore Saxena, Hans J. Haubold, The H- function: theory and application. Springer; 2009.
Bruce J West. Colloquium: Fractional calculus view of complexity: A tutorial, Rev. Mod. Phys. 2014;86:1169.
Richard H. Fractional Calculus: An introduction for Physicists. World Scientific; 2014.
Virginia SK. Generalized fractional calculus and applications. CRC Press; 1993.
Xian feng Z, Darren D, Tawfique H, Jaffrey CB, Bao-Lian Su. Bio-inspired Murray materials for mass transfer and activity, Nature Communications. 2017;8:14921.
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