دانلود کتاب Nonlinear Systems of Fractional Differential Equations

فهرست مطالب :

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