The method of Quasilinearization for scalar Caputo fractional differential equation
DOI:
https://doi.org/10.22399/ijcesen.5041Keywords:
Caputo Fractional differential equation, quasilinearization, upper solution, lower solutionAbstract
Non-linear problems occurring naturally in many branches of science, engineering, etc. are differential equations with integer order derivative. Fractional differential equations (FDEs) may model more effectively certain problems, than ordinary differential equations. Various methods for solving FDEs are being developed and these solutions have great importance in related fields. The method of replacing the original non-linear Caputo fractional differential equation by differential inequalities, whose associated equations can be solved, is known as ‘quasilinearization’. In this paper we establish the method of upper and lower solutions coupled with the method of quasilinearization that converge to the solution of the Caputo fractional differential equation.
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