AIMS Mathematics, 2019, 4(3): 805-820. doi: 10.3934/math.2019.3.805

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The price adjustment equation with different types of conformable derivatives in market equilibrium

Department of Mathematics, Firat University, 23119, Elazig, Turkey

In the current study, price adjustment equation which takes an important place in market equilibrium is presented in consideration of truncated M-derivative including Mittag-Leffler function, beta-derivative and conformable derivative defined in the form of limit for α-differentiable functions. These popular limit-based derivative and integral definitions enable α to vary between (0, 1], whereupon we can observe the intrinsic behavior of the competitive market at different times. The reason of popularity of the underlying definitions is that the natural appearances of their applications. Due to their similarity to classical derivative, it can be taken a good deal of advantages of them in terms of applicability to the diverse governing models. Hence we derive some novel solutions of the marketequilibrium models which are big parts of our lives and in order to solve the linear ordinary differential equations in the sense of M-derivative and beta derivative, the solution methods are given. Moreover, we carry out simulation analysis in order to confirm the usefulness of results obtained.
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© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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