Browsing by Author "Zhamalbekova K."

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    Solving fractional differential equation with Riemann-Liouville fractional derivatives using the Laplace transform
    (SDU University, 2026) Zhamalbekova K.
    Thanks to their ability to capture memory effects in different phenomena, fractional differential equations have become a widely used method in many areas of physics, engineering and applied sciences. This thesis investigates the application of the Laplace transform technique for solving fractional differential equations involving the Riemann–Liouville fractional operator. The study begins with a concise review of fractional calculus theory, with particular emphasis on the definition and properties of the Riemann–Liouville fractional derivative. The Laplace transform is then described as a convenient tool to handle operators of non-integer order. The integration of these two tools enables the development of a systematic technique that transforms the original fractional differential equation into an algebraic equation, thereby facilitating its solution. Solutions to several classes of fractional linear equations are found using Laplace transformations.Many examples show the efficiency of the approach proposed. The results indicate that employing the Laplace transform technique facilitates the solution of fractional differential equations involving the Riemann-Liouville fractional derivative. All things considered, this thesis makes a contribution to the theory of solving fractional differential equations analytically and highlights the effectiveness of Laplace transformation in this case.