On a fractional operator of adjoint hybrid fractional derivative operator

Mine Aylin Bayrak, Ali Demir

Abstract


The achievement of this paper is to propose a new kind of fractional derivative which is called New Constant Proportional Caputo  (NCPC) operator  and to construct the solution of time-fractional initial value problem (TFIVPs) with NCPC derivative by taking the combination of Laplace transform (LT) and Homotopy Analysis method (HAM) into account. Later, the obtained solution is compared with the solutions of TFIVPs with Caputo and  Constant Proportional Caputo  (CPC) derivatives. The gained results reveal that the combination of  LT and HAM together form an efficient method to build the approximate results of TFIVPs in NCPC sense.

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References


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DOI: https://doi.org/10.52846/ami.v51i1.1678