A NOVEL NUMERICAL METHOD for SOLVING MODIFIED ATANGANA-BALEANU FRACTIONAL PROBLEMS BASED on the OPERATIONAL MATRIX METHOD

Lana Abdelhaq; Sondos M. Syam; Muhammed I. Syam

doi:10.1142/S0218348X25400717

A NOVEL NUMERICAL METHOD for SOLVING MODIFIED ATANGANA-BALEANU FRACTIONAL PROBLEMS BASED on the OPERATIONAL MATRIX METHOD

Lana Abdelhaq, Sondos M. Syam, Muhammed I. Syam

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

A novel numerical method for solving modified Atangana-Baleanu fractional problems based on the operational matrix method is presented in this paper. We modify the operational matrix method so that its coefficients can be found in an iterative, direct manner. This avoids solving a large algebraic system, which would be computationally expensive. Several theoretical results are presented, including the existence and uniqueness of the solution for our problem, as well as uniform convergence and error estimates. Examples are provided to demonstrate the efficiency of our numerical approach. Both numerical and theoretical results show that our modified approach works very efficiently. Several applications are discussed.

Original language	English
Article number	2540071
Journal	Fractals
DOIs	https://doi.org/10.1142/S0218348X25400717
Publication status	Accepted/In press - 2025

Keywords

Caputo Type
Fractional Initial Value Problems
Iterative Approach
MABC Derivative
Operational Matrix Method

ASJC Scopus subject areas

Modelling and Simulation
Geometry and Topology
Applied Mathematics

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10.1142/S0218348X25400717

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title = "A NOVEL NUMERICAL METHOD for SOLVING MODIFIED ATANGANA-BALEANU FRACTIONAL PROBLEMS BASED on the OPERATIONAL MATRIX METHOD",

abstract = "A novel numerical method for solving modified Atangana-Baleanu fractional problems based on the operational matrix method is presented in this paper. We modify the operational matrix method so that its coefficients can be found in an iterative, direct manner. This avoids solving a large algebraic system, which would be computationally expensive. Several theoretical results are presented, including the existence and uniqueness of the solution for our problem, as well as uniform convergence and error estimates. Examples are provided to demonstrate the efficiency of our numerical approach. Both numerical and theoretical results show that our modified approach works very efficiently. Several applications are discussed.",

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AU - Syam, Sondos M.

AU - Syam, Muhammed I.

PY - 2025

Y1 - 2025

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AB - A novel numerical method for solving modified Atangana-Baleanu fractional problems based on the operational matrix method is presented in this paper. We modify the operational matrix method so that its coefficients can be found in an iterative, direct manner. This avoids solving a large algebraic system, which would be computationally expensive. Several theoretical results are presented, including the existence and uniqueness of the solution for our problem, as well as uniform convergence and error estimates. Examples are provided to demonstrate the efficiency of our numerical approach. Both numerical and theoretical results show that our modified approach works very efficiently. Several applications are discussed.

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KW - Fractional Initial Value Problems

KW - Iterative Approach

KW - MABC Derivative

KW - Operational Matrix Method

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A NOVEL NUMERICAL METHOD for SOLVING MODIFIED ATANGANA-BALEANU FRACTIONAL PROBLEMS BASED on the OPERATIONAL MATRIX METHOD

Abstract

Keywords

ASJC Scopus subject areas

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