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Hadamard-type fractional differential equations, inclusions and inequalities / / by Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
Hadamard-type fractional differential equations, inclusions and inequalities / / by Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
Autore Ahmad Bashir
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (XIII, 414 p. 1 illus.)
Disciplina 515
Soggetto topico Mathematical analysis
Analysis (Mathematics)
Numerical analysis
Analysis
Numerical Analysis
ISBN 3-319-52141-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Preliminaries -- 2. IVP and BVP for Hadamard-type differential equations and inclusions -- 3. Nonlocal Hadamard fractional boundary value problems -- 4. Fractional integro-differential equations and inclusions -- 5. Fractional differential equations with Hadamard fractional integral conditions -- 6. Hadamard type coupled systems of fractional differential equations -- 7. Nonlinear Langevin equation and inclusions of Hadamard-Caputo type -- 8. Impulsive multi-order Hadamard fractional differential equations -- 9. IVP and BVP for Hybrid Hadamard Fractional Differential Equations and Inclusions -- 10. Positive solutions for Hadamard fractional differential equations on infinite domain -- 11. Fractional integral inequalities via Hadamard's fractional integral -- References -- Index.
Record Nr. UNINA-9910254291503321
Ahmad Bashir  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Nonlinear Systems of Fractional Differential Equations
Nonlinear Systems of Fractional Differential Equations
Autore Ahmad Bashir
Edizione [1st ed.]
Pubbl/distr/stampa Cham : , : Springer, , 2024
Descrizione fisica 1 online resource (597 pages)
Altri autori (Persone) NtouyasSotiris K
ISBN 3-031-62513-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Preliminaries -- 1.1 Definitions and Results from Fractional Calculus -- 1.1.1 Riemann-Liouville and Caputo Fractional Derivative Operators -- 1.1.2 ψ-Riemann-Liouville Fractional Derivative Operator -- 1.1.3 Hilfer Fractional Derivative Operator -- 1.1.4 ψ-Hilfer Fractional Derivative Operator -- 1.1.5 Hadamard Fractional Derivative Operator -- 1.1.6 Hilfer-Hadamard Fractional Derivative Operator -- 1.1.7 Erdélyi-Kober Fractional Integral Operator -- 1.1.8 Generalized (Katugampola) Fractional Derivative Operator -- 1.1.9 k-Riemann-Liouville Fractional Derivative Operator -- 1.1.10 (k,ψ)-Hilfer Fractional Derivative Operator -- 1.1.11 Proportional Fractional Derivative Operator -- 1.1.12 ψ-Proportional Fractional Derivative Operator -- 1.1.13 Hilfer-Proportional Fractional Derivative Operator -- 1.1.14 ψ-Hilfer-Proportional Fractional Derivative Operator -- 1.2 Fixed Point Theorems -- 2 Coupled Multi-point Fractional Differential Systems -- 2.1 On a Fractional Integro-differential System Involving Riemann-Liouville and Caputo Derivatives with Coupled Multi-point Boundary Conditions -- 2.1.1 Existence Results -- 2.1.2 Uniqueness of Solutions -- 2.2 On a Nonlinear System of Riemann-Liouville Fractional Differential Equations with Semi-coupled Integro-multi-point Boundary Conditions -- 2.2.1 Main Results -- 2.3 Fractional Differential Equations with Nonlocal Integral and Integer-Fractional-Order Neumann-Type Boundary Conditions -- 2.3.1 Existence of Solutions -- 2.3.2 Existence and Uniqueness of Solutions -- 2.4 Existence Results for a Coupled System of Caputo-Type Fractional Integro-differential Equations with Multi-point and Sub-strip Boundary Conditions -- 2.4.1 Existence and Uniqueness Results -- 2.4.2 Examples -- 2.5 Notes and Remarks.
3 Existence Results for Coupled Systems of Caputo-Type Sequential Fractional Differential Equations with Nonlocal Integral Boundary Conditions -- 3.1 A Coupled System of Caputo-Type Sequential Fractional Differential Equations with Nonlocal Integral Boundary Conditions -- 3.1.1 Main Results -- 3.2 On a Coupled System of Sequential Fractional Differential Equations with Variable Coefficients and Coupled Integral Boundary Conditions -- 3.2.1 Main Results -- 3.3 Sequential Riemann-Liouville and Hadamard-Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions -- 3.3.1 Main Results -- 3.4 Existence Results for Coupled Nonlinear Sequential Fractional Differential Equations with Coupled Riemann-Stieltjes Integro-Multi-Point Boundary Conditions -- 3.4.1 Main Results -- 3.4.2 Examples -- 3.5 A Six-Point Nonlocal Boundary Value Problem of Nonlinear Coupled Sequential Fractional Integro-differential Equations and Coupled Integral Boundary Conditions -- 3.5.1 Existence and Uniqueness Results -- 3.5.2 Example -- 3.6 Notes and Remarks -- 4 A Study of a Nonlinear Coupled System of Three Fractional Differential Equations with Nonlocal Coupled BoundaryConditions -- 4.1 A Study of a Nonlinear Coupled System of Three Fractional Differential Equations with Nonlocal Coupled Boundary Conditions -- 4.1.1 Main Results -- 4.1.2 Examples -- 4.2 Notes and Remarks -- 5 Existence Results for a Nonlocal Coupled System of Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals -- 5.1 A Coupled System of Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals -- 5.1.1 Existence and Uniqueness Results -- 5.1.2 Example -- 5.2 Notes and Remarks -- 6 Existence Results for Coupled Systems of Nonlinear Multi-term Fractional Differential Equations.
6.1 Existence Results for a Coupled System of Nonlinear Multi-term Fractional Differential Equations with Anti-periodic-Type Coupled Nonlocal Boundary Conditions -- 6.1.1 Existence and Uniqueness Results -- 6.1.2 Mixed Nonlinearities Case -- 6.1.3 Examples -- 6.2 Existence Results for a Coupled System of Differential Equations with Multiple Orders of Fractional Derivatives and Integrals -- 6.2.1 Main Results -- 6.3 Notes and Remarks -- 7 Nonlinear Mixed-Order Coupled Fractional Differential Systems -- 7.1 On a Nonlinear Mixed-Order Coupled Fractional Differential System with New Integral Boundary Conditions -- 7.1.1 Main Results -- 7.1.2 Example -- 7.1.3 A Variant Problem -- 7.2 Coupled Nonlinear Fractional Differential Equations of Different Orders with Nonlocal Coupled Boundary Conditions -- 7.2.1 Main Results -- 7.2.2 Examples -- 7.3 Notes and Remarks -- 8 Investigation of Systems of Hilfer-Type Fractional Differential Equations -- 8.1 System of Hilfer-Hadamard Sequential Fractional Differential Equations with Two-Point Boundary Conditions -- 8.1.1 Existence and Uniqueness Results -- 8.1.2 Existence Result via the Leray-Schauder Alternative -- 8.1.3 Existence and Uniqueness Result via Banach's Fixed Point Theorem -- 8.2 On Coupled Systems for Hilfer Fractional Differential Equations with Nonlocal Integral Boundary Conditions -- 8.2.1 Main Results -- 8.3 On a Nonlocal Coupled System of Hilfer Generalized Proportional Fractional Differential Equations -- 8.3.1 Existence and Uniqueness Results -- 8.3.2 Existence Results in Banach Space -- 8.3.3 Examples -- 8.4 Coupled Systems of Hilfer-Type Sequential Fractional Differential Equations with Riemann-Stieltjes Integral Multi-Strip Boundary Conditions -- 8.4.1 A Subsidiary Result -- 8.4.2 Existence and Uniqueness Result via Banach's Fixed-Point Theorem.
8.4.3 Existence Result via the Leray-Schauder Alternative -- 8.4.4 Existence Result via Krasnosel'skiĭ's Fixed-Point Theorem -- 8.4.5 Examples -- 8.5 A Study of Coupled Systems of ψ-Hilfer-Type Sequential Fractional Differential Equations with Integro-Multipoint Boundary Conditions -- 8.5.1 An Auxiliary Result -- 8.5.2 Existence and Uniqueness Results -- 8.5.3 Existence and Uniqueness Result via Banach's Fixed-Point Theorem -- 8.5.4 Existence Result via the Leray-Schauder Alternative -- 8.5.5 Existence Result via Krasnosel'skiĭ's Fixed-Point Theorem -- 8.6 A Nonlocal Boundary Value Problem of Coupled Sequential ψ-Hilfer Fractional Differential Equations -- 8.6.1 Main Results -- 8.7 Nonlocal Coupled Systems for (k,φ)-Hilfer Fractional Differential Equations -- 8.7.1 Existence and Uniqueness Results -- 8.7.2 Existence of a Unique Solution -- 8.7.3 Existence Results -- 8.7.4 Illustrative Examples -- 8.8 On a Nonlinear Coupled System of Differential Equations Involving Hilfer Fractional Derivative and Riemann-Liouville Mixed Operators with Nonlocal Integro-Multipoint Boundary Conditions -- 8.8.1 Existence and Uniqueness Results -- 8.8.2 Examples -- 8.9 Notes and Remarks -- 9 Coupled Systems of Sequential Caputo and Hadamard Fractional Differential Equations with Coupled Separated Boundary Conditions -- 9.1 Coupled Systems of Sequential Caputo and Hadamard Fractional Differential Equations with Coupled Separated Boundary Conditions -- 9.1.1 Main Results -- 9.1.2 Examples -- 9.2 Notes and Remarks -- 10 On Nonlinear Systems of Fractional Langevin Equations with Boundary Conditions -- 10.1 A Nonlinear System of Riemann-Liouville-Type Fractional Langevin Equations with Generalized Nonlocal Fractional Integral Boundary Conditions -- 10.1.1 Main Results -- 10.1.2 Existence Result via Krasnosel'skiĭ's Fixed Point Theorem.
10.1.3 Existence Result via O'Regan's Fixed Point Theorem -- 10.2 Systems of Generalized Sturm-Liouville and Langevin Fractional Differential Equations -- 10.3 Notes and Remarks -- 11 A System of Fractional Differential Equations with Erdélyi-Kober Fractional Integral Conditions -- 11.1 A System of Fractional Differential Equations with Nonlocal Erdélyi-Kober Fractional Integral Conditions -- 11.2 Notes and Remarks -- 12 Positive Solutions for Fractional Differential Systems with Nonlocal Riemann-Liouville Fractional Integral Boundary Conditions -- 12.1 Positive Solutions for Nonlocal Riemann-Liouville Fractional Differential Systems -- 12.2 Notes and Remarks -- 13 A Langevin-Type q-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal BoundaryConditions -- 13.1 A Langevin-Type q-Variant Nonlocal Nonlinear Fractional System -- 13.1.1 Existence and Uniqueness Result -- 13.1.2 Existence Result -- 13.1.3 Examples -- 13.2 Notes and Remarks -- 14 A Coupled System of Nonlinear Fractional q-Integro-Difference Equations with q-Integral Coupled Boundary Conditions -- 14.1 Existence Results for a Coupled System of Nonlinear Fractional q-Integro-Difference Equations with q-Integral Coupled Boundary Conditions -- 14.1.1 Main Results -- 14.2 Notes and Remarks -- References -- Index.
Record Nr. UNINA-9910878049103321
Ahmad Bashir  
Cham : , : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui