Fractional Difference Differential Equations and Inclusions Analysis and Stability 1st Edition by Saïd Abbas, Bashir Ahmad, Mouffak Benchohra, Abdelkrim Salim ISBN 0443236011 978-0443236013

Fractional Difference Differential Equations and Inclusions Analysis and Stability 1st Edition by Saïd Abbas, Bashir Ahmad, Mouffak Benchohra, Abdelkrim Salim- Ebook PDF Instant Download/Delivery: 0443236011, 978-0443236013

Full download Fractional Difference Differential Equations and Inclusions Analysis and Stability 1st Edition after payment

 

Product details:

ISBN 10: 0443236011 

ISBN 13: 978-0443236013

Author: Saïd Abbas, Bashir Ahmad, Mouffak Benchohra, Abdelkrim Salim

 Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Covered equations include delay effects of finite, infinite, or state-dependent nature, and tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness, as well as the measure of weak noncompactness. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. All abstract results in the book are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences.

Table of contents: 

1: Introduction

Abstract

References

2: Preliminary background

Abstract

2.1. Notations and definitions

2.2. Elements from fractional calculus theory

2.3. Fractional q-calculus

2.4. Multi-valued analysis

2.5. Measure of noncompactness

2.6. Measure of weak noncompactness

2.7. Degree of nondensifiability

2.8. Some attractivity concepts

2.9. Some Ulam stability concepts

2.10. Some fixed-point theorems

2.11. Auxiliary lemmas

References

3: Caputo fractional difference equations in Banach spaces

Abstract

3.1. Implicit fractional q-difference equations in Banach spaces

3.2. Fractional q-difference equations on the half line

3.3. On the solution of Caputo fractional q-difference equations in Banach spaces

3.4. Notes and remarks

References

4: Caputo fractional difference inclusions

Abstract

4.1. Fractional q-difference inclusions in Banach spaces

4.2. Weak solutions for Pettis fractional q-difference inclusions

4.3. Upper and lower solutions for fractional q-difference inclusions

4.4. Notes and remarks

References

5: Ulam stability for fractional difference equations

Abstract

5.1. Existence and Ulam stability for implicit fractional q-difference equations

5.2. Ulam stability results

5.3. Implicit fractional q-difference equations: analysis and stability

5.4. Uniqueness and Ulam stability for implicit fractional q-difference equations via Picard operators theory

5.5. Notes and remarks

References

6: Impulsive fractional difference equations

Abstract

6.1. Impulsive implicit Caputo fractional q-difference equations

6.2. Implicit Caputo fractional q-difference equations with noninstantaneous impulses

6.3. Instantaneous and noninstantaneous impulsive integro-differential equations in Banach spaces

6.4. Notes and remarks

References

7: Coupled fractional difference systems

Abstract

7.1. Implicit coupled Caputo fractional q-difference systems

7.2. Existence and oscillation for coupled fractional q-difference systems

7.3. Notes and remarks

References

8: Coupled Caputo–Hadamard fractional differential systems in generalized Banach spaces

Abstract

8.1. Coupled Caputo–Hadamard fractional differential systems with multipoint boundary conditions

8.2. Random coupled Caputo–Hadamard fractional differential systems with four-point boundary conditions

8.3. Random coupled systems of implicit Caputo–Hadamard fractional differential equations with multi-point boundary conditions

8.4. Notes and remarks

References

9: Coupled Hilfer–Hadamard fractional differential systems in generalized Banach spaces

Abstract

9.1. Coupled Hilfer and Hadamard fractional differential systems

9.2. Coupled Hilfer and Hadamard random fractional differential systems with finite delay

9.3. Random coupled Hilfer and Hadamard fractional differential systems

9.4. Notes and remarks

References

10: Oscillation and nonoscillation results for fractional q-difference equations and inclusions

Abstract

10.1. Oscillation and nonoscillation results for Caputo fractional q-difference equations and inclusions

10.2. Existence and oscillation for coupled fractional q-difference systems

10.3. Notes and remarks

References

11: A Filippov’s theorem and topological structure of solution sets for fractional q-difference inclusions

Abstract

11.1. Existence and topological structure of solution sets

11.2. Filippov theorem

11.3. Notes and remarks

References

12: On ψ-Caputo fractional differential equations in Banach spaces

Abstract

12.1. Boundary value problem for fractional differential equations via densifiability techniques

12.2. Application of Meir–Keeler condensing operators

12.3. Notes and remarks

References

13: Ulam stability for ψ-Caputo fractional differential equations and systems

Abstract

13.1. Existence and Mittag–Leffler–Ulam stability of fractional partial differential equations

13.2. Coupled system of fractional differential equations without and with delay in generalized Banach spaces

13.3. Coupled system of nonlinear hyperbolic partial fractional differential equations in generalized Banach spaces

13.4. Notes and remarks

References

14: Monotone iterative technique for ψ-Caputo fractional differential equations

Abstract

14.1. Initial value problem for nonlinear ψ-Caputo fractional differential equations

14.2. Sequential ψ-Caputo fractional differential equations with nonlinear boundary conditions

14.3. Hyperbolic fractional partial differential equation

14.4. Notes and remarks

People also search for:

finite difference methods for fractional differential equations
the finite difference methods for fractional ordinary differential equations
fractional differential equations examples
fractional differential equations definition
types of fractional differential equations

Tags: Saïd Abbas, Bashir Ahmad, Mouffak Benchohra, Abdelkrim Salim, Fractional Difference, Differential Equations, Inclusions Analysis, Stability