On the solutions of nonlinear fractional partial differential equation arising in mathematical biology / Fatima Hathat

Public ISBD Titre : On the solutions of nonlinear fractional partial differential equation arising in mathematical biology Type de document : document électronique Auteurs : Fatima Hathat, Auteur ; Khalouta,Ali, Directeur de thèse Editeur : Setif:UFA Année de publication : 2026 Importance : 1 vol (107 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Fractional partial differential equations Caputo fractional derivative Khalouta transform Index. décimale : 510 - Mathématique Résumé : Fractional partial differential equations as generalizations of classical integer partial differential equations are used to model many real-world problems. The main motivation of this thesis is to propose a novel analytical technique for solving the nonlinear time-fractional biological population model The proposed technique utilizes the Khalouta transform and the reduced differential transform to construct the approximate analytical solution of the proposed model. Three numerical applications are presented to illustrate the efficiency and accuracy of the proposed method. Note de contenu : Sommaire Introductioniv 1 Fundamentalsoffractionalcalculustheory1 1.1Fractionalsystemsandtheirapplications................... 1 1.1.1Automaticsystems............................ 1 1.1.2Physics.................................. 2 1.1.3Mechanicsofcontinuousmedia..................... 2 1.1.4Acoustics................................. 3 1.2Functionalspaces................................. 3 1.2.1Spacesofintegrablefunctions...................... 3 1.2.2Spacesofcontinuousandabsolutelycontinuousfunctions....... 4 1.2.3Spacesofcontinuousfunctionswithweights.............. 5 1.2.4Fixedpointtheorem........................... 5 1.3Specialfunctionsforfractionalderivation.................... 6 1.3.1TheGammafunction........................... 6 1.3.2TheBêtafunction............................ 7 1.3.3TheMittag-Le­erfunction....................... 7 1.4Fractionalintegralsandderivatives....................... 8 1.4.1FractionalintegralinthesenseofRiemann-Liouville......... 8 1.4.2FractionalderivativeinthesenseofRiemann–Liouville........ 12 1.4.3PropertiesofthefractionalderivativeintheRiemann-Liouvillesense 15 1.4.4FractionalderivativeintheCaputosense................ 18 1.4.5PropertiesofthefractionalderivativeintheCaputosense...... 22 1.4.6RelationshipbetweentheRiemann-LiouvilleandCaputoapproaches. 23 2 Existenceanduniquenesstheoremforfractionaldi¤erentialequationwith Caputofractionalderivative25 2.1EquivalencebetweentheFDEandtheVolterraintegralequation....... 26 2.2Existenceanduniquenesstheorem........................ 27 3 Approximateanalyticaltechniquesandtheirapplications33 3.1Adomiandecompositiontechnique(ADT)................... 33 3.1.1BasicideaofADT............................ 33 3.1.2Adomianpolynomials........................... 35 3.1.3ConvergenceanalysisofADT...................... 36 3.2Homotopyperturbationtechnique(HPT).................... 40 3.2.1BasicideaofHPT............................ 40 3.2.2ConvergenceanalysisofHPT...................... 41 3.3Variationaliterationtechnique(VIT)...................... 49 3.3.1BasicideaofVIT............................. 49 3.3.2AlternativeapproachtoVIT....................... 50 3.3.3ConvergenceanalysisofVIT....................... 52 3.4Daftardar-Gejji-Jafaritechnique(DGJT).................... 57 3.4.1BasicideaofDGJT............................ 57 3.4.2ConvergenceanalysisofDGJT...................... 58 4 SolvingnonlinearCaputotime-fractionalpartialdi¤erentialequations62 4.1AnalysisoftheADT............................... 63 4.2AnalysisoftheHPT............................... 67 4.3AnalysisoftheVIT................................ 71 4.4AnalysisoftheDGJT.............................. 74 5 Anovelhybridtechniquetoresolvethenonlineartime-fractionalbiologi- calpopulationmodel 79 5.1Mathematicalformulationofthenonlineartime-fractionalbiologicalpopula- tionmodel..................................... 79 5.2Khaloutatransform(KHT)........................... 81 5.3Reduceddi¤erentialtransformmethod(RDTM)................ 84 5.4Khaloutareduceddi¤erentialtransformmethod(KHRDTM)......... 86 5.5ConvergenceanalysisoftheKHRDTM..................... 87 5.6Applicationsandnumericalresults....................... 89 Conclusionandresearchperspectives101 Côte titre : DM/0225 On the solutions of nonlinear fractional partial differential equation arising in mathematical biology [document électronique] / Fatima Hathat, Auteur ; Khalouta,Ali, Directeur de thèse . - [S.l.] : Setif:UFA, 2026 . - 1 vol (107 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Fractional partial differential equations Caputo fractional derivative Khalouta transform Index. décimale : 510 - Mathématique Résumé : Fractional partial differential equations as generalizations of classical integer partial differential equations are used to model many real-world problems. The main motivation of this thesis is to propose a novel analytical technique for solving the nonlinear time-fractional biological population model The proposed technique utilizes the Khalouta transform and the reduced differential transform to construct the approximate analytical solution of the proposed model. Three numerical applications are presented to illustrate the efficiency and accuracy of the proposed method. Note de contenu : Sommaire Introductioniv 1 Fundamentalsoffractionalcalculustheory1 1.1Fractionalsystemsandtheirapplications................... 1 1.1.1Automaticsystems............................ 1 1.1.2Physics.................................. 2 1.1.3Mechanicsofcontinuousmedia..................... 2 1.1.4Acoustics................................. 3 1.2Functionalspaces................................. 3 1.2.1Spacesofintegrablefunctions...................... 3 1.2.2Spacesofcontinuousandabsolutelycontinuousfunctions....... 4 1.2.3Spacesofcontinuousfunctionswithweights.............. 5 1.2.4Fixedpointtheorem........................... 5 1.3Specialfunctionsforfractionalderivation.................... 6 1.3.1TheGammafunction........................... 6 1.3.2TheBêtafunction............................ 7 1.3.3TheMittag-Le­erfunction....................... 7 1.4Fractionalintegralsandderivatives....................... 8 1.4.1FractionalintegralinthesenseofRiemann-Liouville......... 8 1.4.2FractionalderivativeinthesenseofRiemann–Liouville........ 12 1.4.3PropertiesofthefractionalderivativeintheRiemann-Liouvillesense 15 1.4.4FractionalderivativeintheCaputosense................ 18 1.4.5PropertiesofthefractionalderivativeintheCaputosense...... 22 1.4.6RelationshipbetweentheRiemann-LiouvilleandCaputoapproaches. 23 2 Existenceanduniquenesstheoremforfractionaldi¤erentialequationwith Caputofractionalderivative25 2.1EquivalencebetweentheFDEandtheVolterraintegralequation....... 26 2.2Existenceanduniquenesstheorem........................ 27 3 Approximateanalyticaltechniquesandtheirapplications33 3.1Adomiandecompositiontechnique(ADT)................... 33 3.1.1BasicideaofADT............................ 33 3.1.2Adomianpolynomials........................... 35 3.1.3ConvergenceanalysisofADT...................... 36 3.2Homotopyperturbationtechnique(HPT).................... 40 3.2.1BasicideaofHPT............................ 40 3.2.2ConvergenceanalysisofHPT...................... 41 3.3Variationaliterationtechnique(VIT)...................... 49 3.3.1BasicideaofVIT............................. 49 3.3.2AlternativeapproachtoVIT....................... 50 3.3.3ConvergenceanalysisofVIT....................... 52 3.4Daftardar-Gejji-Jafaritechnique(DGJT).................... 57 3.4.1BasicideaofDGJT............................ 57 3.4.2ConvergenceanalysisofDGJT...................... 58 4 SolvingnonlinearCaputotime-fractionalpartialdi¤erentialequations62 4.1AnalysisoftheADT............................... 63 4.2AnalysisoftheHPT............................... 67 4.3AnalysisoftheVIT................................ 71 4.4AnalysisoftheDGJT.............................. 74 5 Anovelhybridtechniquetoresolvethenonlineartime-fractionalbiologi- calpopulationmodel 79 5.1Mathematicalformulationofthenonlineartime-fractionalbiologicalpopula- tionmodel..................................... 79 5.2Khaloutatransform(KHT)........................... 81 5.3Reduceddi¤erentialtransformmethod(RDTM)................ 84 5.4Khaloutareduceddi¤erentialtransformmethod(KHRDTM)......... 86 5.5ConvergenceanalysisoftheKHRDTM..................... 87 5.6Applicationsandnumericalresults....................... 89 Conclusionandresearchperspectives101 Côte titre : DM/0225

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
DM/0225	DM/0225	Thèse	Bibliothèque des sciences	Arabe	Disponible Disponible

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