Solution of Fractional Order Equations in the Domain of the Mellin Transform
Keywords:Caputo fractional derivative, Fractional calculus, Mellin transform, Miller-Ross fractional derivative, Riemann-Liouville fractional derivative, Riemann-Liouville fractional integral
This paper presents the Mellin transform for the solution of the fractional order equations. The Mellin transform approach occurs in many areas of applied mathematics and technology. The Mellin transform of fractional calculus of different flavours; namely the Riemann-Liouville fractional derivative, Riemann-Liouville fractional integral, Caputo fractional derivative and the Miller-Ross sequential fractional derivative were obtained. Three illustrative examples were considered to discuss the applications of the Mellin transform and its fundamental properties. The results show that the Mellin transform is a good analytical method for the solution of fractional order equations.
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