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

Öz In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. 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 and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.
Anahtar Kelimeler:

## Collocation points, fractional derivative, graph theory, matching polynomial, matrix method

#### Kaynak Göster

 Bibtex @ { tbtkmath575269, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2019}, volume = {43}, pages = {373 - 392}, doi = {}, title = {A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types}, key = {cite}, author = {Kürkçü, Ömür Kivanç and Aslan, Ersin and Sezer, Mehmet} } APA Kürkçü, Ö , Aslan, E , Sezer, M . (2019). A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types . Turkish Journal of Mathematics , 43 (1) , 373-392 . MLA Kürkçü, Ö , Aslan, E , Sezer, M . "A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types" . Turkish Journal of Mathematics 43 (2019 ): 373-392 < Chicago Kürkçü, Ö , Aslan, E , Sezer, M . "A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types". Turkish Journal of Mathematics 43 (2019 ): 373-392 RIS TY - JOUR T1 - A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types AU - Ömür Kivanç Kürkçü , Ersin Aslan , Mehmet Sezer Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 373 EP - 392 VL - 43 IS - 1 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER - EndNote %0 Turkish Journal of Mathematics A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types %A Ömür Kivanç Kürkçü , Ersin Aslan , Mehmet Sezer %T A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 1 %R %U ISNAD Kürkçü, Ömür Kivanç , Aslan, Ersin , Sezer, Mehmet . "A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types". Turkish Journal of Mathematics 43 / 1 (Şubat 2019): 373-392 . AMA Kürkçü Ö , Aslan E , Sezer M . A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types. Turkish Journal of Mathematics. 2019; 43(1): 373-392. Vancouver Kürkçü Ö , Aslan E , Sezer M . A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types. Turkish Journal of Mathematics. 2019; 43(1): 373-392. IEEE Ö. Kürkçü , E. Aslan ve M. 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", Turkish Journal of Mathematics, c. 43, sayı. 1, ss. 373-392, Şub. 2019