A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types

Ömür Kıvanç KÜRKÇÜ; Ersin ASLAN; Mehmet SEZER

A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types

Date

2019

Authors

Ömür Kıvanç KÜRKÇÜ

Ersin ASLAN

Mehmet SEZER

Abstract

In this study, we introduce multidelay fractional differential equations with variable coefficients in a uniqueformula. A novel graph-operational matrix method based on the fractional Caputo, Riemann–Liouville, Caputo–Fabrizio,and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points andmatrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractionalderivative types is more appropriate for the method. The solutions of model problems are improved via a new residualerror analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulnessof the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.