What does this research mean for the field?

The Fractional Explicit Method (FEM), which integrates Lagrange interpolation into a third-order Adams-Bashforth approach, provides a reliable and efficient numerical framework for solving Caputo fractional differential equations with nonuniform step sizes. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To develop and evaluate a variable-step numerical method based on the third-order Adams–Bashforth scheme for solving Caputo fractional differential equations.

September 10, 2026Mathematical Methods in the Applied SciencesOpen Access

A Variable Step Third‐Order Adams–Bashforth Method for Caputo Fractional Differential Equations

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Authors

MPMahendra Pichkiya EMEkta Mittal DSD. L. Suthar

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Overview

Computational modeling demonstrates reliable numerical solutions for Caputo fractional differential equations using variable time steps, highlighting improved flexibility for complex dynamic systems.

Key Points

To develop and evaluate a variable-step numerical method based on the third-order Adams–Bashforth scheme for solving Caputo fractional differential equations.
Formulated the Fractional Explicit Method (FEM) by coupling a third-order Adams–Bashforth framework with Lagrange interpolation to approximate history terms across nonuniform step sizes.
Derived the order of accuracy, convergence properties, and conditional stability using a linear test equation, benchmarking performance against an established fractional predictor–corrector method.
Demonstrated practical utility by applying the method to simulate a fractional dynamical model of smoking habit dynamics.
Theoretical analysis confirmed the method maintains third-order accuracy and convergence when evaluated with nonuniform temporal step sizes.
Numerical tests showed the explicit variable-step approach performs reliably and efficiently relative to standard predictor–corrector formulations.
Dynamical simulations of the smoking habit model successfully captured population behavioral trends across varied time intervals.

Cite This Study

Pichkiya et al. (2026) studied this question.

synapsesocial.com/papers/6aa27b4758559d80afc746c8 https://doi.org/10.1002/mma.70959

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September 10, 2026Mathematical Methods in the Applied SciencesOpen Access

A Variable Step Third‐Order Adams–Bashforth Method for Caputo Fractional Differential Equations

View Full Paper

Ask AI

Bookmark

Authors

MPMahendra Pichkiya EMEkta Mittal DSD. L. Suthar

Discussion

Member takes

Overview

Computational modeling demonstrates reliable numerical solutions for Caputo fractional differential equations using variable time steps, highlighting improved flexibility for complex dynamic systems.

Key Points

To develop and evaluate a variable-step numerical method based on the third-order Adams–Bashforth scheme for solving Caputo fractional differential equations.
Formulated the Fractional Explicit Method (FEM) by coupling a third-order Adams–Bashforth framework with Lagrange interpolation to approximate history terms across nonuniform step sizes.
Derived the order of accuracy, convergence properties, and conditional stability using a linear test equation, benchmarking performance against an established fractional predictor–corrector method.
Demonstrated practical utility by applying the method to simulate a fractional dynamical model of smoking habit dynamics.
Theoretical analysis confirmed the method maintains third-order accuracy and convergence when evaluated with nonuniform temporal step sizes.
Numerical tests showed the explicit variable-step approach performs reliably and efficiently relative to standard predictor–corrector formulations.
Dynamical simulations of the smoking habit model successfully captured population behavioral trends across varied time intervals.

Cite This Study

Pichkiya et al. (2026) studied this question.

synapsesocial.com/papers/6aa27b4758559d80afc746c8 https://doi.org/10.1002/mma.70959

View Full Paper

Ask AI

Bookmark