Fractional Interpretation of Anomalous Diffusion and Semiconductor Equations

Abstract

Fractional calculus is considered as an effective tool in representing differential equations and systems. Fractional differential equations are generalizations of ordinary differential equations to an arbitrary non integer order. The idea of Fractional Differential Equations are used to analyse the semiconductor equations. Application of fractional calculus will add additional nonlinearity and can be used to model more complex phenomena. In this work, the fractional calculus computations are done using matrix approach and algorithams are implemented in MATLAB. The pn junction characteristics is simulated for fractional orders. As the order reaches its integer equivalents, normal semiconductor behaviour is obtained, validating the simulated results. The pn junction characteristics is simulated for fractional order and deviation from the actual characteristics for various fractional orders are analysed.