Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method

•We applied HPM for solving time-fractional PDEs with proportional delay.•Convergence theorem of method and maximum truncation error are given.•Some examples are solved by HPM. In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of α are presented graphically.