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Browsing by Author "Johnston, Sarah Jane"

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    On Ritz Approximation For A Class Of Fractional Optimal Control Problems
    (2022) Baleanu, Dumitru; Jafari, Hossein; Johnston, Sarah Jane; Baleanu, Dumitru; 56389
    We apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the boundary and initial conditions. The ultimate goal of the algorithm is to set up a system of equations whose number matches the unknowns. Computing the unknowns enables us to approximate the solution of the objective function in the form of polynomials.
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    Results for Mild solution of fractional coupled hybrid boundary value problems
    (Sciendo, 2015) Baleanu, Dumitru; Jafari, Hossein; Khan, Hasib; Johnston, Sarah Jane; 56389
    The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray-Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.