Computational solution of fractional pantograph equation with varying delay term

Delay Differential Equations DDEs have great importance in real life phenomena. Among them is a special type of equation known as Pantograph Delay Differential Equation PDDE. Such kind of equations cannot be solved using ordinary methods, and hence, it becomes a challenge when the complexity increases, especially if one wants to study Fractional Pantograph Delay Differential Equation (FPDDE). In this work, FPDDEs with a general Delay term is solved numerically by an iteration method called Perturbation Iteration Algorithm (PIA). It is based on the Taylor series and elim-inates the non-linear terms easily. Iterative results are discussed in detail in both tabular and graphical forms. A graphical interpre-tation of the variability of the Delay term is also provided for a deeper understanding of its range.