A Novel Approach to Solve Nonlinear Higher Order Fractional Volterra–Fredholm Integro‐Differential Equations Using Laplace Adomian Decomposition Method
ABSTRACT This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi‐analytically treat nonlinear integro‐fractional differential equations of the Volterra–Fredholm–Hammerstein type. The higher‐order fractional derivative will be expressed in the Caputo se...
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| Published in | International journal of numerical modelling Vol. 38; no. 2 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Inc
01.03.2025
Wiley Subscription Services, Inc |
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| Online Access | Get full text |
| ISSN | 0894-3370 1099-1204 |
| DOI | 10.1002/jnm.70040 |
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| Abstract | ABSTRACT
This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi‐analytically treat nonlinear integro‐fractional differential equations of the Volterra–Fredholm–Hammerstein type. The higher‐order fractional derivative will be expressed in the Caputo sense, and the first‐order simple degenerate and the difference kernel will be used. With this approach, the inverse Laplace transform is applied, and the solution of the equation is viewed as the sum of an endless series of components that usually converge to the solution. Numerical applications frequently employ a shortened number of terms when a closed‐form solution is not possible. Lastly, a diagram displaying the arrived at and discussed solutions was shown along with illustrative examples. |
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| AbstractList | ABSTRACT
This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi‐analytically treat nonlinear integro‐fractional differential equations of the Volterra–Fredholm–Hammerstein type. The higher‐order fractional derivative will be expressed in the Caputo sense, and the first‐order simple degenerate and the difference kernel will be used. With this approach, the inverse Laplace transform is applied, and the solution of the equation is viewed as the sum of an endless series of components that usually converge to the solution. Numerical applications frequently employ a shortened number of terms when a closed‐form solution is not possible. Lastly, a diagram displaying the arrived at and discussed solutions was shown along with illustrative examples. This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi‐analytically treat nonlinear integro‐fractional differential equations of the Volterra–Fredholm–Hammerstein type. The higher‐order fractional derivative will be expressed in the Caputo sense, and the first‐order simple degenerate and the difference kernel will be used. With this approach, the inverse Laplace transform is applied, and the solution of the equation is viewed as the sum of an endless series of components that usually converge to the solution. Numerical applications frequently employ a shortened number of terms when a closed‐form solution is not possible. Lastly, a diagram displaying the arrived at and discussed solutions was shown along with illustrative examples. |
| Author | Sharif, Abdulrahman A. Ghadle, Kirtiwant P. Hamood, Maha M. |
| Author_xml | – sequence: 1 givenname: Maha M. orcidid: 0009-0003-0657-2093 surname: Hamood fullname: Hamood, Maha M. email: maha.mohammed@taiz.edu.ye organization: Taiz University – sequence: 2 givenname: Abdulrahman A. orcidid: 0000-0001-9076-3615 surname: Sharif fullname: Sharif, Abdulrahman A. organization: Hodeidah University – sequence: 3 givenname: Kirtiwant P. surname: Ghadle fullname: Ghadle, Kirtiwant P. organization: Dr. Babasaheb Ambedkar Marathwada University |
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| Cites_doi | 10.1007/978-3-642-21449-3 10.24996/ijs.2019.60.10.15 10.1016/j.amc.2012.12.072 10.1016/S0304-0208(06)80001-0 10.1007/978-3-319-78458-8_5 10.1016/j.heliyon.2024.e25903 10.1016/j.amc.2011.01.007 10.1007/978-1-4757-1466-1 10.5269/bspm.v36i4.31478 10.1016/j.rinam.2024.100504 10.1016/j.amc.2006.07.102 |
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| References | 2021; 48 2011; 217 2021; 22 2011 2007; 186 2006 2024; 10 2011; 13 1971 2008; 4 2024; 14 1979 2020; 8 2019; 60 2013; 219 2013; 12 2022; 12 2019 1999; 198 1983 2020; 45 2022; 1 2014 2024; 24 2022; 11 2016; 29 2012; 6 2018; 36 2022; 245 Parand K. (e_1_2_8_5_1) 2016; 29 Masti I. (e_1_2_8_12_1) 2024; 14 Brown L. (e_1_2_8_22_1) 2021; 22 e_1_2_8_25_1 Yavuz M. (e_1_2_8_8_1) 2020; 8 Sharif A. (e_1_2_8_18_1) 2022; 11 Atanackovic T. M. (e_1_2_8_27_1) 2014 e_1_2_8_3_1 Lee S. (e_1_2_8_23_1) 2022; 245 Badawi H. (e_1_2_8_4_1) 2022; 1 e_1_2_8_7_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_20_1 Tajadodi H. (e_1_2_8_13_1) 2022; 12 mith J. (e_1_2_8_21_1) 2020; 45 Jerri A. J. (e_1_2_8_16_1) 1971 Manafianheris J. (e_1_2_8_32_1) 2012; 6 Ahmed S. S. (e_1_2_8_17_1) 2019; 60 e_1_2_8_19_1 Podlubny I. (e_1_2_8_26_1) 1999 Mittal R. C. (e_1_2_8_14_1) 2008; 4 e_1_2_8_15_1 Yang C. (e_1_2_8_28_1) 2013; 12 Chen X. (e_1_2_8_24_1) 2021; 48 Yavuz M. (e_1_2_8_10_1) 2019 Golub G. H. (e_1_2_8_29_1) 1983 Wazwaz A. M. (e_1_2_8_2_1) 2011 e_1_2_8_11_1 Arife A. S. (e_1_2_8_31_1) 2011; 13 e_1_2_8_30_1 |
| References_xml | – year: 2011 – volume: 12 start-page: 160 issue: 2 year: 2022 end-page: 168 article-title: Genocchi Polynomials as a Tool for Solving a Class of Fractional Optimal Control Problems publication-title: Theories & Applications – volume: 1 year: 2022 article-title: Fractional Conformable Stochastic Integrodifferential Equations: Existence, Uniqueness, and Numerical Simulations Utilizing the Shifted Legendre Spectral Collocation Algorithm publication-title: Hindawi Mathematical Problems in Engineering – volume: 22 start-page: 567 issue: 3 year: 2021 end-page: 580 article-title: Combining Analytical and Numerical Approaches for Efficient Problem Solving publication-title: Computational Physics Review – year: 1983 – volume: 36 start-page: 33 issue: 4 year: 2018 end-page: 54 article-title: System of Nonlinear Volterra Integro‐Differential Equations of Arbitrary Order publication-title: Boletim da Sociedade Paranaense de Matematica – volume: 8 start-page: 142 issue: 1 year: 2020 end-page: 154 article-title: Analysis of an Epidemic Spreading Model With Exponential Decay Law publication-title: Mathematical Sciences and Applications E‐Notes – volume: 60 start-page: 2207 issue: 10 year: 2019 end-page: 2222 article-title: Laplace Adomian and Laplace Modified Adomian Decomposition Methods for Solving Nonlinear Integro‐Fractional Differential Equations of the Volterra‐Hammerstein Type publication-title: Iraqi Journal of Science – volume: 6 start-page: 41 issue: 1 year: 2012 end-page: 55 article-title: Solving the Integro‐Differential Equations Using the Modified Laplace Adomian Decomposition Method publication-title: Journal of Mathematical Extension – year: 1971 – volume: 219 start-page: 6750 year: 2013 end-page: 6760 article-title: Numerical Solution of Fractional Integro‐Differential Equations by a Hybrid Collocation Method publication-title: Applied Mathematics and Computation – volume: 198 year: 1999 – year: 1979 – volume: 4 start-page: 87 issue: 42 year: 2008 end-page: 94 article-title: Solution of Fractional Integro‐Differential Equations by Adomian Decomposition Method publication-title: International Journal of Applied Mathematics and Mechanics – year: 2014 – volume: 14 start-page: 12 issue: 1 year: 2024 end-page: 19 article-title: On Analyzing Two Dimensional Fractional Order Brain Tumor Modelbased on Orthonormal Bernoulli Polynomials and Newton's Method publication-title: Theories & Applications – volume: 10 year: 2024 article-title: Existence, Uniqueness, and Galerkin Shifted Legendre's Approximation of Time Delays Integrodifferential Models by Adapting the Hilfer Fractional Attitude publication-title: Heliyon – volume: 12 start-page: 1173 year: 2013 end-page: 1183 article-title: Numerical Solution of Integro‐Differential Equations of Fractional Order by Laplace Decomposition Method publication-title: WSEAS Transactions on Mathematics – volume: 217 start-page: 6337 year: 2011 end-page: 6348 article-title: Convenient Analytic Recurrence Algorithms for the Adomian Polynomials publication-title: Applied Mathematics and Computation – volume: 45 start-page: 123 issue: 2 year: 2020 end-page: 134 article-title: Semi‐Analytic Methods in Engineering Applications publication-title: Journal of Engineering Science – volume: 29 start-page: 895 issue: 4 year: 2016 end-page: 907 article-title: Operational Matrices to Solve Nonlinear Volterra‐Fredholm Integro‐Differential Equations of Multi‐Arbitrary Order publication-title: Gazi University Journal of Science – volume: 186 start-page: 286 year: 2007 end-page: 293 article-title: Generalized Taylor's Formula publication-title: Applied Mathematics and Computation – year: 2006 – volume: 13 start-page: 756 issue: 4 year: 2011 end-page: 761 article-title: Laplace Adomian Decomposition Method for Solving a Model Chronic Myelogenous Leukemia CML and T Cell Interaction publication-title: World Applied Sciences Journal – volume: 11 start-page: 97 issue: 1 year: 2022 end-page: 106 article-title: On ‐Caputo Fractional Nonlinear Volterra‐Fredholm Integro Differential Equations publication-title: Discontinuity, Nonlinearity and Complexity – volume: 48 start-page: 350 issue: 4 year: 2021 end-page: 362 article-title: Innovations in Semi‐Analytic Modeling for Engineering Problems publication-title: International Journal of Engine Research – volume: 245 start-page: 112 issue: 1 year: 2022 end-page: 126 article-title: Advancements in Semi‐Analytic Solutions for Complex Systems publication-title: Applied Mathematics and Computation – year: 2019 – volume: 24 year: 2024 article-title: Existence, Uniqueness, and Collocation Solutions Using the Shifted Legendre Spectral Method for the Hilfer Fractional Stochastic Integro‐Differential Equations Regarding Stochastic Brownian Motion publication-title: Results in Applied Mathematics – volume: 45 start-page: 123 issue: 2 year: 2020 ident: e_1_2_8_21_1 article-title: Semi‐Analytic Methods in Engineering Applications publication-title: Journal of Engineering Science – volume-title: Linear and Nonlinear Integral Equations, Methods and Application year: 2011 ident: e_1_2_8_2_1 doi: 10.1007/978-3-642-21449-3 – volume: 60 start-page: 2207 issue: 10 year: 2019 ident: e_1_2_8_17_1 article-title: Laplace Adomian and Laplace Modified Adomian Decomposition Methods for Solving Nonlinear Integro‐Fractional Differential Equations of the Volterra‐Hammerstein Type publication-title: Iraqi Journal of Science doi: 10.24996/ijs.2019.60.10.15 – volume: 12 start-page: 160 issue: 2 year: 2022 ident: e_1_2_8_13_1 article-title: Genocchi Polynomials as a Tool for Solving a Class of Fractional Optimal Control Problems publication-title: Theories & Applications – ident: e_1_2_8_19_1 doi: 10.1016/j.amc.2012.12.072 – volume: 245 start-page: 112 issue: 1 year: 2022 ident: e_1_2_8_23_1 article-title: Advancements in Semi‐Analytic Solutions for Complex Systems publication-title: Applied Mathematics and Computation – ident: e_1_2_8_3_1 doi: 10.1016/S0304-0208(06)80001-0 – volume: 48 start-page: 350 issue: 4 year: 2021 ident: e_1_2_8_24_1 article-title: Innovations in Semi‐Analytic Modeling for Engineering Problems publication-title: International Journal of Engine Research – volume-title: New Numerical Techniques for Solving Fractional Partial Differential Equations in Conformable Sense year: 2019 ident: e_1_2_8_10_1 doi: 10.1007/978-3-319-78458-8_5 – volume-title: Introduction to Integral Equations With Applications year: 1971 ident: e_1_2_8_16_1 – ident: e_1_2_8_6_1 doi: 10.1016/j.heliyon.2024.e25903 – volume: 29 start-page: 895 issue: 4 year: 2016 ident: e_1_2_8_5_1 article-title: Operational Matrices to Solve Nonlinear Volterra‐Fredholm Integro‐Differential Equations of Multi‐Arbitrary Order publication-title: Gazi University Journal of Science – ident: e_1_2_8_20_1 doi: 10.1016/j.amc.2011.01.007 – ident: e_1_2_8_15_1 doi: 10.1007/978-1-4757-1466-1 – volume: 6 start-page: 41 issue: 1 year: 2012 ident: e_1_2_8_32_1 article-title: Solving the Integro‐Differential Equations Using the Modified Laplace Adomian Decomposition Method publication-title: Journal of Mathematical Extension – volume-title: Error Analysis of Least Squares Algorithms year: 1983 ident: e_1_2_8_29_1 – volume: 14 start-page: 12 issue: 1 year: 2024 ident: e_1_2_8_12_1 article-title: On Analyzing Two Dimensional Fractional Order Brain Tumor Modelbased on Orthonormal Bernoulli Polynomials and Newton's Method publication-title: Theories & Applications – volume: 22 start-page: 567 issue: 3 year: 2021 ident: e_1_2_8_22_1 article-title: Combining Analytical and Numerical Approaches for Efficient Problem Solving publication-title: Computational Physics Review – volume-title: Mathematics in Science and Engineering year: 1999 ident: e_1_2_8_26_1 – volume: 12 start-page: 1173 year: 2013 ident: e_1_2_8_28_1 article-title: Numerical Solution of Integro‐Differential Equations of Fractional Order by Laplace Decomposition Method publication-title: WSEAS Transactions on Mathematics – ident: e_1_2_8_30_1 – ident: e_1_2_8_11_1 doi: 10.5269/bspm.v36i4.31478 – volume-title: Fractional Calculus With Applications in Mechanics year: 2014 ident: e_1_2_8_27_1 – volume: 8 start-page: 142 issue: 1 year: 2020 ident: e_1_2_8_8_1 article-title: Analysis of an Epidemic Spreading Model With Exponential Decay Law publication-title: Mathematical Sciences and Applications E‐Notes – volume: 4 start-page: 87 issue: 42 year: 2008 ident: e_1_2_8_14_1 article-title: Solution of Fractional Integro‐Differential Equations by Adomian Decomposition Method publication-title: International Journal of Applied Mathematics and Mechanics – ident: e_1_2_8_7_1 doi: 10.1016/j.rinam.2024.100504 – volume: 11 start-page: 97 issue: 1 year: 2022 ident: e_1_2_8_18_1 article-title: On ψ$$ \psi $$‐Caputo Fractional Nonlinear Volterra‐Fredholm Integro Differential Equations publication-title: Discontinuity, Nonlinearity and Complexity – ident: e_1_2_8_9_1 – volume: 1 year: 2022 ident: e_1_2_8_4_1 article-title: Fractional Conformable Stochastic Integrodifferential Equations: Existence, Uniqueness, and Numerical Simulations Utilizing the Shifted Legendre Spectral Collocation Algorithm publication-title: Hindawi Mathematical Problems in Engineering – ident: e_1_2_8_25_1 doi: 10.1016/j.amc.2006.07.102 – volume: 13 start-page: 756 issue: 4 year: 2011 ident: e_1_2_8_31_1 article-title: Laplace Adomian Decomposition Method for Solving a Model Chronic Myelogenous Leukemia CML and T Cell Interaction publication-title: World Applied Sciences Journal |
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This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi‐analytically treat nonlinear... This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi‐analytically treat nonlinear integro‐fractional... |
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| SubjectTerms | Adomian decomposition method Decomposition Differential equations Fractional calculus integro‐fractional Volterra Fredholm higher order Laplace transform Laplace transforms |
| Title | A Novel Approach to Solve Nonlinear Higher Order Fractional Volterra–Fredholm Integro‐Differential Equations Using Laplace Adomian Decomposition Method |
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