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