Fractional Mechanical Oscillator

TABLE OF CONTENTS Title Page i Certificate of Approval ii Dedication iii Acknowledgment iv Abstract v Table of contents vi 1. FRACTIONAL ORDER CALCULUS 2. FUNCTIONS OF FRACTIONAL CALCULUS 2.1 The Gamma function 3 2.2 The Beta Function 5 2.3 The Mittag-Leffler Function 5 2.4 Laplace Transform 7 2.5 The Convolution Theorem 9 2.6 Riemann-Liouville Fractional integral 10 2.7 Riemann-Liouville Fractional derivative 13 2.8 The Caputo’s Fractional Derivative 14 2.9 Laplace Transform of Fractional Integral 19 2.1.1 Laplace Transform of Riemann-Liouville Fractional Derivative 20 2.1.2 Laplace Transform…