Annals of Mathematical Sciences and Applications

Volume 6 (2021)

Number 2

Computational solution of fractional pantograph equation with varying delay term

Pages: 121 – 144

DOI: https://dx.doi.org/10.4310/AMSA.2021.v6.n2.a1

Authors

M. Khalid (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi, Pakistan)

S. K. Fareeha (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi, Pakistan)

S. Mariam (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi, Pakistan)

Abstract

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 eliminates the non-linear terms easily. Iterative results are discussed in detail in both tabular and graphical forms. A graphical interpretation of the variability of the Delay term is also provided for a deeper understanding of its range.

Keywords

perturbation iteration algorithm, fractional delay differential equation, series solution, fractional calculus

2010 Mathematics Subject Classification

Primary 34K37, 65L03. Secondary 81-05, 93C23, 97M50.

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Received 12 March 2021

Accepted 2 April 2021

Published 18 October 2021