Solution of a Fractional Order Two Point Boundary Value Problem using Reflection Operator
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Date
2022
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Department of Electrical Engineering, NITS
Abstract
A scheme for fractional order two point boundary value problem formulation and solution using Reflection operator and Grunwald-letnikov approximation is presented in this work .The fractional derivative (FD) is defined in terms of Riemann-Liouville sense. The dynamic system constraint is in the form of a fractional differential equation that includes integer derivative in addition to the fractional derivatives. The quadratic performance index considered as a function of both the state and the control variables. In the performance index all variables are considered as scalar values. A direct numerical technique based on Grunwald-Letnikov (GL) approximation is used to solve the resulting equations first we convert right FD into left FD by using reflection operator and then apply GL formulation. The order of the fractional derivatives is taken as less than one.