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A COMPUTATIONAL ALGORITHM for the NUMERICAL SOLUTION of NONLINEAR FRACTIONAL INTEGRAL EQUATIONS

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dc.contributor.authorAmin, Rohul
dc.contributor.authorSenu, Norazak
dc.contributor.authorHafeez, Muhammad Bilal
dc.contributor.authorArshad, Noreen Izza Bt
dc.contributor.authorAhmadian, Ali
dc.contributor.authorSalahshour, Soheil
dc.contributor.authorSumelka, Wojciech
dc.contributor.institutionAmin, Rohul, Department of Mathematics, University of Peshawar, Peshawar, Pakistan
dc.contributor.institutionSenu, Norazak, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
dc.contributor.institutionHafeez, Muhammad Bilal, Institute of Structural Analysis, Politechnika Poznanska, Poznan, Poland
dc.contributor.institutionArshad, Noreen Izza Bt, Department of Computer and Information Science, Universiti Teknologi PETRONAS, Seri Iskandar, Malaysia
dc.contributor.institutionAhmadian, Ali, Institute of IR 4.0, Universiti Kebangsaan Malaysia, Bangi, Malaysia, Department of Mathematics, Yakın Doğu Üniversitesi, Nicosia, Cyprus
dc.contributor.institutionSalahshour, Soheil, Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
dc.contributor.institutionSumelka, Wojciech, Institute of Structural Analysis, Politechnika Poznanska, Poznan, Poland
dc.date.accessioned2025-10-05T15:20:37Z
dc.date.issued2022
dc.description.abstractIn this paper, we develop a numerical method for the solution of nonlinear fractional integral equations (NFIEs) based on Haar wavelet collocation technique (HWCT). Under certain conditions, we also prove the uniqueness and existence as well as Hyers-Ulam (HU) stability of the solution. With the help of the mentioned technique, the considered problem is transformed to a system of algebraic equations which is then solved for the required results by using Broyden algorithm. To check the validation and convergence of the proposed technique, some examples are given. For different number of collocation points (CPs), maximum absolute and mean square root errors are computed. The results show that for solving these equations, the HWCT is effective. The convergence rate is also measured for different CPs, which is nearly equal to 2. © 2024 Elsevier B.V., All rights reserved.
dc.identifier.doi10.1142/S0218348X22400308
dc.identifier.issn17936543
dc.identifier.issn0218348X
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85122038583
dc.identifier.urihttps://doi.org/10.1142/S0218348X22400308
dc.identifier.urihttps://hdl.handle.net/20.500.14719/8909
dc.identifier.volume30
dc.language.isoen
dc.publisherWorld Scientific
dc.relation.sourceFractals
dc.subject.authorkeywordsCps
dc.subject.authorkeywordsHwct
dc.subject.authorkeywordsNfies
dc.subject.authorkeywordsUniqueness And Existence
dc.subject.authorkeywordsIntegral Equations
dc.subject.authorkeywordsNonlinear Equations
dc.subject.authorkeywordsCollocation Points
dc.subject.authorkeywordsCollocation Techniques
dc.subject.authorkeywordsCondition
dc.subject.authorkeywordsEquation Based
dc.subject.authorkeywordsFractional Integral Equations
dc.subject.authorkeywordsHaar Wavelet Collocation Technique
dc.subject.authorkeywordsHaar-wavelets
dc.subject.authorkeywordsHyers-ulam Stability
dc.subject.authorkeywordsNonlinear Fractional Integral Equation
dc.subject.authorkeywordsUniqueness And Existence
dc.subject.authorkeywordsNumerical Methods
dc.subject.indexkeywordsIntegral equations
dc.subject.indexkeywordsNonlinear equations
dc.subject.indexkeywordsCollocation points
dc.subject.indexkeywordsCollocation techniques
dc.subject.indexkeywordsCondition
dc.subject.indexkeywordsEquation based
dc.subject.indexkeywordsFractional integral equations
dc.subject.indexkeywordsHaar wavelet collocation technique
dc.subject.indexkeywordsHaar-wavelets
dc.subject.indexkeywordsHyers-Ulam stability
dc.subject.indexkeywordsNonlinear fractional integral equation
dc.subject.indexkeywordsUniqueness and existence
dc.subject.indexkeywordsNumerical methods
dc.titleA COMPUTATIONAL ALGORITHM for the NUMERICAL SOLUTION of NONLINEAR FRACTIONAL INTEGRAL EQUATIONS
dc.typeArticle
dcterms.referencesWazwaz, Abdul Majid 1., A first course in integral equations, second edition, pp. 1-312, (2015), Yang, Zhanwen, Blow-up behavior of Hammerstein-type delay Volterra integral equations, Frontiers of Mathematics in China, 8, 2, pp. 261-280, (2013), Al-Khaled, Kamel M., Numerical approximations for population growth models, Applied Mathematics and Computation, 160, 3, pp. 865-873, (2005), Bellour, Azzeddine, A Taylor collocation method for solving delay integral equations, Numerical Algorithms, 65, 4, pp. 843-857, (2014), Castro, L. P., Hyers–ulam–rassias stability for a class of nonlinear volterra integral equations, Banach Journal of Mathematical Analysis, 3, 1, pp. 36-43, (2009), Acta Univ Apulensis Math Inform, (2011), J Nonlinear Sci Appl, (2017), Ali, Zeeshan, Ulam stability results for the solutions of nonlinear implicit fractional order differential equations, Hacettepe Journal of Mathematics and Statistics, 48, 4, pp. 1092-1109, (2019), Yousefi, A., A computational approach for solving fractional integral equations based on Legendre collocation method, Mathematical Sciences, 13, 3, pp. 231-240, (2019), Ren, Yong, Existence results for fractional order semilinear integro-differential evolution equations with infinite delay, Integral Equations and Operator Theory, 67, 1, pp. 33-49, (2010)
dspace.entity.typePublication
local.indexed.atScopus
person.identifier.scopus-author-id55176957400
person.identifier.scopus-author-id55670963500
person.identifier.scopus-author-id60033157300
person.identifier.scopus-author-id25824626100
person.identifier.scopus-author-id59760609700
person.identifier.scopus-author-id23028598900
person.identifier.scopus-author-id26435543200

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