<![CDATA[This paper investigates the application of the Laplace transform method in solving fractional differential equations. It establishes sufficient conditions under which the Laplace transform provides a rational approach to these problems. Key definitions and properties of fractional calculus, including the Riemann-Liouville and Caputo fractional derivatives, are discussed. Several lemmas are proved to facilitate the computation of inverse Laplace transforms involving fractional operators. The effectiveness of the method is demonstrated through examples of solving linear fractional differential equations with exact solutions. The study concludes that while the Laplace transform is well-suited for fractional differential equations with constant coefficients, its applicability is limited by the nature of the forcing terms.]]>
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