Solution of Inhomogeneous Linear Fractional Differential Equations Involving Jumarie Fractional Derivative
DOI:
https://doi.org/10.3329/jsr.v15i2.62040Abstract
This paper presents a method for solving inhomogeneous linear sequential fractional differential equations with constant coefficients (ILSFDE) involving Jumarie fractional derivatives in terms of Mittag-Leffler functions. For this purpose, the fundamental properties of the Jumarie derivative and Mittag-Leffler functions are given. After this, the successive jumarie fractional derivatives of Mittag-Leffler functions, fractional cosine, and sine functions are obtained. Further, we determined the particular integrals of these functions and then found the complete solutions of ILSFDE. in terms of Mittag-Leffler functions, fractional cosine, and sine functions. We have demonstrated this developed method with a few examples of ILSFDE. This method is similar to the method for finding the complete solutions of classical differential equations with constant coefficients.
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