Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix

Khodabandehlo, Hamid Reza; Shivanian, Elyas; Abbasbandy, Saeid

doi:10.1007/s00366-021-01422-7

Cited by 3 publications

(2 citation statements)

References 52 publications

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“…The Reproducing kernel Hilbert Space method to solve nonlinear F DDEs have employed via Ghasemi et al [21]. In have [8] authors provided a new numerical method for solving FDDEs and Khodabandehlo et al in [1][2][3] have proposed a N SJOM technique for nonlinear variable-order F DDEs.…”

Section: Introductionmentioning

confidence: 99%

A Novel Shifted Jacobi Operational Matrix Method for Linear Multi-terms Delay Differential Equations of Fractional Variable-order with Periodic and Anti-periodic Conditions

KHODABANDEHLO,

SHIVANIAN,

ABBASBANDY

2024

KgJMat

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This paper investigates the generalized linear multi-terms delay fractional diﬀerential equation of variable order with periodic and anti-periodic conditions. In this work, a novel shifted Jacobi operational matrix technique is applied to solve a class of these equations, so that the original problem becomes a system of algebraic equations that can be solved by numerical methods. The proposed technique is successfully applied to the aforementioned problem. Suﬃcient and complete numerical tests are presented to demonstrate the accuracy, generality, eﬃciency of presented technique and the ﬂexibility of this scheme. The numerical results of this method are compared with other existing methods such as fractional backward diﬀerential formulas (FBDF). Comparing the outcomes of these schemes, as well as comparing the current technique (NSJOM) with the exact solution, demonstrates the eﬃciency and validity of this method. It should be noted that the implementation of current method is considered very easy and general for many numerical techniques. Furthermore, the error and its bound are estimated.

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Section: Introductionmentioning

confidence: 99%

A Novel Shifted Jacobi Operational Matrix Method for Linear Multi-terms Delay Differential Equations of Fractional Variable-order with Periodic and Anti-periodic Conditions

KHODABANDEHLO,

SHIVANIAN,

ABBASBANDY

2024

KgJMat

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“…As a result of these considerations, the authors have decided to use the ADS (Adams) and ERK (explicit Runge-Kutta) numerical solvers to solve the delay differential system [52][53][54][55][56]. The Adams predictor-corrector approach [46,[57][58][59][60] is also a more efficient and straightforward numerical tool for solving delay differential systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical treatment for mathematical model of farming awareness in crop pest management

Anwar,

Ahmad,

Kiani

et al. 2023

Front. Appl. Math. Stat.

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The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios.

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Fractional Jacobi Kernel Functions: Theory and Application

Rasanan

Rad

Tameh

et al. 2023

Industrial and Applied Mathematics

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Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix

Cited by 3 publications

References 52 publications

A Novel Shifted Jacobi Operational Matrix Method for Linear Multi-terms Delay Differential Equations of Fractional Variable-order with Periodic and Anti-periodic Conditions

A Novel Shifted Jacobi Operational Matrix Method for Linear Multi-terms Delay Differential Equations of Fractional Variable-order with Periodic and Anti-periodic Conditions

Numerical treatment for mathematical model of farming awareness in crop pest management

Fractional Jacobi Kernel Functions: Theory and Application

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