A novel study for solving systems of nonlinear fractional integral equations

Syam, Sondos M.; Siri, Z.; Altoum, Sami H.; Adam Aigo, Musa; Kasmani, R. Md.

doi:10.1080/27690911.2023.2277738

Applied Mathematics in Science and Engineering

2023

DOI: 10.1080/27690911.2023.2277738

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A novel study for solving systems of nonlinear fractional integral equations

Sondos M. Syam,

Z. Siri,

Sami H. Altoum

et al.

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2024

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Cited by 4 publications

References 31 publications

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An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

Irandoust‐Pakchin,

Hossein Derakhshan,

Rezapour

et al. 2024

Math Methods in App Sciences

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In this manuscript, we study and examine the time‐fractional modified anomalous sub‐diffusion model of distributed‐order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second‐order difference method based on the L1 formula for the temporal variable. In this case, stability and convergence analysis for time discretization using the L1 formula is displayed. For the second approach, we display and demonstrate the numerical method for the full‐discrete based on the Galerkin weak form based on various kernels and shape functions of reproducing kernel particle method which do not have the ‐Kronecker property. Moreover, in this manuscript, in order to be able to use the necessary boundary conditions, the two straight strategies are used: one is the Lagrange multiplier method, and the other one is the penalty method. By using penalty method, we can the main boundary value model is changed to a new BVP with Robin boundary condition. At the end of the article, some numerical examples are presented and analyzed for the efficiency of the proposed numerical method. Also, the presented numerical method is compared with other numerical approaches, and the results of this comparison are reported in the form of a table.

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An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

Irandoust‐Pakchin,

Hossein Derakhshan,

Rezapour

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

An efficient technique for time fractional Klein-Gordon equation based on modified Laplace Adomian decomposition technique via hybridized Newton-Raphson Scheme arises in relativistic fractional quantum mechanics

Sahu,

Jena

2024

Partial Differential Equations in Applied Mathematics

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An efficient numerical method for two-dimensional fractional integro-differential equations with modified Atangana–Baleanu fractional derivative using operational matrix approach

Abdelhaq,

Syam,

Syam

2024

Partial Differential Equations in Applied Mathematics

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A novel study for solving systems of nonlinear fractional integral equations

Cited by 4 publications

References 31 publications

An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

An efficient technique for time fractional Klein-Gordon equation based on modified Laplace Adomian decomposition technique via hybridized Newton-Raphson Scheme arises in relativistic fractional quantum mechanics

An efficient numerical method for two-dimensional fractional integro-differential equations with modified Atangana–Baleanu fractional derivative using operational matrix approach

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