Analytical solutions of a time-fractional system of proportional delay differential equations

In our physical settings, most of the problems encountered are nonlinear in nature whose solutions can better be captured in fractional space. In this paper, a semi-analytical method is proposed for the approximate-analytical solutions of certain system of time-fractional differential equations (TFDDEs) prompted by proportional delays. The proposed semi-analytical technique is built on the basis of the classical transformation method. The effectiveness and reliability of the proposed technique is illustratively demonstrated and the results are compared with their exact forms. It is remarked that using this method, the TFDDEs with proportional delays need not be converted to SFDEs with constant delays before obtaining their solutions, and no symbolic calculation is required.