SOLUTIONS OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS OF ORDER 𝒏−𝟏<𝒏𝒒<𝒏

Abstract

In this study, the linear Caputo fractional differential equation of order 𝑛−1<𝑛𝑞<𝑛 is investigated. First, the solution of the equation of order 0<𝑞<1, with variable coefficients, is obtained by using the solution of differential equation of integer order which is the least integer greater than fractional order. Moreover, the solution of linear fractional differential equations of order 𝑛−1<𝑛𝑞<𝑛 is considered. The solutions of the equation are presented in terms of Mittag-Leffler function with three parameters. The main goal of this study is to present a closed-series form of the solutions. To demonstrate the accuracy and the effectiveness of the proposed approach, some numerical solutions are given.

Keywords

• Fractional Differential Equation
• Mittag-Leffler function
• Three parameters

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