Fractional Calculus in Solving Engineering Problems

Fractional calculus is a rapidly growing field both in theory and applications in the real world problems to explain several physical phenomena. Fractional order system or systems containing fractional derivatives and integration which has a non- local character. The present paper discusses several definitions of fractional derivatives including a discussion of notation, operators in the sense of Riemann-Liouville, Caputo, Grunwald- Letnikov etc. The concept of fractional order differential equation is also introduced. A specific problem on ordinary fractional order differential equation related to RC circuit with semi-infinite lossy transmission line is studied. A very new approach Adomain Decomposition Method (ADM) is utilized to solve the problem. Index Terms - Fractional Differential Equation; Generalized dynamic system; Adomain Decomposition method.