[HTML][HTML] A novel analytical method for the multi-delay fractional differential equations through the matrix of clique polynomials of the cocktail party graph

AN Nirmala, S Kumbinarasaiah - Results in Control and Optimization, 2023 - Elsevier
This paper provides a unique graph matrix approach based on the Clique polynomials of the
Cocktail party graph to effectively solve multi-delay fractional differential equations (MDFDE) …

Gegenbauer wavelet solutions of fractional integro-differential equations

G Özaltun, A Konuralp, S Gümgüm - Journal of Computational and Applied …, 2023 - Elsevier
The aim of this study is to use Gegenbauer wavelets in the solution of fractional integro-
differential equations. The method is applied to several problems with different values of …

A fast numerical method for fractional partial integro-differential equations with spatial-time delays

E Aslan, ÖK Kürkçü, M Sezer - Applied Numerical Mathematics, 2021 - Elsevier
This study aims to efficiently solve the space-time fractional partial integro-differential
equations with spatial-time delays, employing a fast numerical methodology dependent …

A new Bell function approach to solve linear fractional differential equations

Ş Yüzbaşı - Applied Numerical Mathematics, 2022 - Elsevier
In this study, a new collocation approach based on the Bell polynomials is presented to
solve linear fractional differential equations. The aim of this study is to find the approximate …

Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials

Ş Yüzbaşı, G Yıldırım - … Journal of Nonlinear Sciences and Numerical …, 2023 - degruyter.com
In this study, a collocation approach is presented to solve Bagley–Torvik equation, which is
a class of fractional differential equations. As most fractional differential equations do not …

An advanced method with convergence analysis for solving space-time fractional partial differential equations with multi delays

Ö Kıvanç Kürkçü, E Aslan, M Sezer - The European Physical Journal Plus, 2019 - Springer
This study considers the space-time fractional partial differential equations with multi delays
under a unique formulation, proposing a numerical method involving advanced matrix …

On the numerical solution of fractional differential equations with cubic nonlinearity via matching polynomial of complete graph

ÖK Kürkçü, Eİ Aslan, M Sezer - Sādhanā, 2019 - Springer
This study deals with a generalized form of fractional differential equations with cubic
nonlinearity, employing a matrix-collocation method dependent on the matching polynomial …

An integrated numerical method with error analysis for solving fractional differential equations of quintic nonlinear type arising in applied sciences

ÖK Kürkçü, E Aslan, M Sezer - Mathematical Methods in the …, 2019 - Wiley Online Library
In this study, fractional differential equations having quintic nonlinearity are considered by
proposing an accurate numerical method based on the matching polynomial and matrix …

[PDF][PDF] A NOVEL ANALYTICAL METHOD FOR TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION THROUGH CLIQUE POLYNOMIALS OF THE COCKTAIL …

MA Bayrak, A Demir, A Büyük - Journal of Applied Analysis & …, 2025 - jaac-online.com
This paper is devoted to providing a new approach to solve time fractional convection-
diffusion equation (TFCDE) by utilizing Clique polynomials of the Cocktail party graph and …

[PDF][PDF] Results in Control and Optimization

AN Nirmala, S Kumbinarasaiah - researchgate.net
Models of nonlinear partial differential equations are essential in the theoretical sciences,
especially Physics and Mathematics. It is exceedingly challenging to arrive at an analytical …