Modeling with fractional difference equations

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Abstract

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.

Keywords

Discrete fractional calculus
Fractional summation by parts
Calculus of variations

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Graduate student.