Modeling with fractional difference equations

In this paper, we develop some basics of discrete fractional calculus such as Leibniz rule and summation by parts formula. We define simplest discrete fractional calculus of variations problem and derive Euler–Lagrange equation. We introduce and solve Gompertz fractional difference equation for tumo...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 369; no. 1; pp. 1 - 9
Main Authors: ATICI, Ferhan M, SENGÜL, Sevgi
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.09.2010
Elsevier
Subjects:
Calculus of variations
Calculus of variations and optimal control
Difference and functional equations, recurrence relations
Discrete fractional calculus
Exact sciences and technology
Finite differences and functional equations
Fractional summation by parts
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Discrete fractional calculus
Calculus of variations
Fractional summation by parts
Euler Lagrange equation
Mathematical analysis
Variational calculus
Difference equation
Summation
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:In this paper, we develop some basics of discrete fractional calculus such as Leibniz rule and summation by parts formula. We define simplest discrete fractional calculus of variations problem and derive Euler–Lagrange equation. We introduce and solve Gompertz fractional difference equation for tumor growth models.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.02.009