Abstract
In this paper, we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, the analytical solution for a class of fractional models associated with the logistic model, the von Foerster model and the Bertalanffy model is presented graphically for various fractional orders. The solution of the corresponding classical model is recovered as a particular case.
Highlights
Fractional calculus is a generalization of ordinary calculus, where derivatives and integrals of arbitrary order are defined
Abdeljawad [14] introduced a method based on the conformable Laplace transform technique; it is suitable for a large class of initial value problems for fractional differential equations
Motivated by applications of fractional integral inequalities, we study the reliability of the conformable Laplace transform method for solving linear fractional differential equations with constant coefficients: (α)
Summary
Fractional calculus is a generalization of ordinary calculus, where derivatives and integrals of arbitrary (non-integer) order are defined. The concept of fractional operators has been introduced almost simultaneously with the development of the classical ones. The idea of these operators first appeared in a letter between L’Hopital and Leibniz in which the question of a half-order derivative was posed [1–3]. All of them satisfy the following important properties: fractional operators are linear, that is if L is a fractional derivative, : L( f + kg) = L( f ) + kL( g) for any functions f , g ∈ C n [ a, b] and k ∈ R.
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