Solving fractional variable-order differential equations for Generalized Caputo-type with time-varying delay by using the operation matrix method

Citation

Shloof, A. M. and Basim, M. and Abd Alaziz, Ali and Senu, N. and Aljensh, A. and Ahmadian, A. (2026) Solving fractional variable-order differential equations for Generalized Caputo-type with time-varying delay by using the operation matrix method. Nonlinear Functional Analysis and Applications, 31 (2). pp. 561-579. ISSN 1229-1595; eISSN: 2466-0973

Abstract

This study introduces novel derivative and integral operators derived from newly formulated generalized Caputo fractional derivatives (GCFDs). A numerical approach is developed utilizing these operators to solve variable-order fractional differential equations with time-varying delay (VOFDETVD). The approach entails approximating the solutions of VOFDETVD by employing shifted Legendre polynomials (SLPs) as basis vectors. To assess the efficiency of the numerical method, tests are conducted on various examples, with different values of α specified for the fractional differential operator of the new generalized Caputo. Moreover, the present method is comprehensively evaluated for robustness and effectiveness through comparisons with existing approaches.

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Additional Metadata

Item Type:	Article
Subject:	Analysis
Subject:	Numerical Analysis
Subject:	Control and Optimization
Divisions:	Faculty of Science Institute for Mathematical Research
DOI Number:	https://doi.org/10.22771/nfaa.2026.31.02.17
Publisher:	Kyungnam University Press
Keywords:	Fractional delay differential equations; generalized Caputo fractional derivatives; operational matrix; SLPs
Sustainable Development Goals (SDGs):	SDG 9: Industry, Innovation and Infrastructure, SDG 4: Quality Education, SDG 17: Partnerships for the Goals
Depositing User:	Ms. Siti Radziah Mohamed@mahmod
Date Deposited:	28 Jul 2026 10:08
Last Modified:	28 Jul 2026 10:08
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.22771/nfaa.2026.31.02.17
URI:	http://psasir.upm.edu.my/id/eprint/127358
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