Muutke küpsiste eelistusi

E-raamat: Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

, , ,
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Mar-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319521411
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 135,84 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Hadamard-Type Fractional Differential Equations, Inclusions and InequalitiesSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Mar-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319521411
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. This book is a useful resource for readers and researchers interested in the area of fractional calculus.

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.

Arvustused

The book offers a comprehensive study of the above-mentioned problems, based, in a consistent manner, on the recent studies of the authors, as well as on some relevant results in fractional calculus literature of the last decade. a nice documented study, very useful for graduate and post-graduate students and for researchers interested in nonlinear applied analysis in general, and fractional analysis in particular. (Adrian Petruel, Mathematical Reviews, November, 2017)

In this nicely written monograph, the authors present a comprehensive treatment of the application of the Hadamard-type fractional derivative to both fractional differential equations and fractional differential inclusions. this book is very well written and is enjoyable to read. For researchers who have a basic grasp of the fundamentals of the fractional calculus, this book will provide a wealth of ideas for research projects and, more generally, hours of interesting and worthwhile reading. (Christopher Goodrich, zbMATH 1370.34002, 2017)

1 Preliminaries
1(12)
1.1 Definitions and Results from Multivalued Analysis
1(2)
1.2 Definitions and Results from Fractional Calculus
3(3)
1.3 Fixed Point Theorems
6(7)
2 IVP and BVP for Hadamard-Type Differential Equations and Inclusions
13(32)
2.1 Introduction
13(1)
2.2 Functional and Neutral Fractional Differential Equations
13(9)
2.2.1 Functional Differential Equations
15(3)
2.2.2 Neutral Functional Differential Equations
18(3)
2.2.3 An Example
21(1)
2.3 Functional and Neutral Fractional Differential Inclusions
22(8)
2.3.1 Functional Differential Inclusions
22(5)
2.3.2 Neutral Functional Differential Inclusions
27(2)
2.3.3 Examples
29(1)
2.4 BVP for Fractional Order Hadamard-type Functional Differential Equations and inclusions
30(13)
2.4.1 Fractional Order Hadamard-Type Functional Differential Equations
31(6)
2.4.2 Fractional Order Hadamard-Type Functional Differential Inclusions
37(6)
2.5 Notes and Remarks
43(2)
3 Nonlocal Hadamard Fractional Boundary Value Problems
45(42)
3.1 Introduction
45(1)
3.2 A Three-Point Hadamard-Type Fractional Boundary Value Problem
46(8)
3.2.1 The Case of Fractional Integral Boundary Conditions
52(2)
3.3 Nonlocal Hadamard BVP of Fractional Integro-Differential Equations
54(11)
3.3.1 Existence and Uniqueness Result via Banach's Fixed Point Theorem
56(3)
3.3.2 Existence Result via Krasnoselskii's Fixed Point Theorem
59(1)
3.3.3 Existence Result via Leray-Schauder's Nonlinear Alternative
60(2)
3.3.4 Existence Result via Leray-Schauder's Degree
62(2)
3.3.5 A Companion Problem
64(1)
3.4 Nonlocal Hadamard BVP of Fractional Integro-Differential Inclusions
65(9)
3.4.1 The Caratheodory Case
65(5)
3.4.2 The Lower Semicontinuous Case
70(1)
3.4.3 The Lipschitz Case
71(3)
3.5 Nonlocal Hadamard Fractional Boundary Value Problems
74(1)
3.6 Existence Results: The Single-Valued Case
75(4)
3.7 Existence Result: The Multivalued Case
79(6)
3.8 Notes and Remarks
85(2)
4 Fractional Integro-Differential Equations and Inclusions
87(22)
4.1 Introduction
87(1)
4.2 Mixed Hadamard and Riemann-Liouville Fractional Integro-Differential Equations
87(8)
4.3 Mixed Hadamard and Riemann-Liouville Fractional Integro-Differential Inclusions
95(10)
4.3.1 The Upper Semicontinuous Case
96(4)
4.3.2 The Lipschitz Case
100(3)
4.3.3 Examples
103(2)
4.4 Existence Result via Endpoint Theory
105(3)
4.5 Notes and Remarks
108(1)
5 Factional Differential Equations with Hadamard Fractional Integral Conditions
109(64)
5.1 Introduction
109(1)
5.2 Nonlocal Hadamard Fractional Differential Equations
109(13)
5.2.1 Existence and Uniqueness Result via Banach's Fixed Point Theorem
111(2)
5.2.2 Existence and Uniqueness Result via Banach's Fixed Point Theorem and Holder's Inequality
113(2)
5.2.3 Existence and Uniqueness Result via Nonlinear Contractions
115(1)
5.2.4 Existence Result via Krasnoselskii's Fixed Point Theorem
116(2)
5.2.5 Existence Result via Leray-Schauder's Nonlinear Alternative
118(2)
5.2.6 Existence Result via Leray-Schauder's Degree Theory
120(2)
5.3 Nonlocal Hadamard Fractional Differential Inclusions
122(9)
5.3.1 The Lipschitz Case
123(3)
5.3.2 The Caratheodory Case
126(4)
5.3.3 The Lower Semicontinuous Case
130(1)
5.4 Nonlocal Hadamard Fractional Boundary Value Problems
131(13)
5.4.1 Existence Results: The Single-Valued Case
132(5)
5.4.2 Existence Results: The Multivalued Case
137(7)
5.5 Multiple Hadamard Fractional Integral Conditions
144(11)
5.6 Riemann-Liouville Fractional Differential Inclusions
155(7)
5.6.1 The Caratheodory Case
155(4)
5.6.2 The Lower Semicontinuous Case
159(1)
5.6.3 The Lipschitz Case
159(3)
5.7 Hadamard Nonlocal Fractional Integral Boundary Value Problems
162(10)
5.8 Notes and Remarks
172(1)
6 Coupled Systems of Hadamard and Riemann-Liouville Fractional Differential Equations with Hadamard Type Integral Boundary Conditions
173(36)
6.1 Introduction
173(1)
6.2 A Fully Hadamard Type Integral Boundary Value
173(8)
6.3 A Coupled System of Riemann-Liouville Fractional Differential Equations with Coupled and Uncoupled Hadamard Fractional Integral Boundary Conditions
181(15)
6.3.1 Coupled Integral Boundary Conditions Case
181(12)
6.3.2 Uncoupled Integral Boundary Conditions Case
193(3)
6.4 Multiple Hadamard Fractional Integral Conditions for Coupled Systems
196(12)
6.5 Notes and Remarks
208(1)
7 Nonlinear Langevin Equation and Inclusions Involving Hadamard-Caputo Type Fractional Derivatives
209(54)
7.1 Introduction
209(1)
7.2 Nonlinear Langevin Equation Case
209(17)
7.2.1 Existence and Uniqueness Result via Banach's Fixed Point Theorem
213(4)
7.2.2 Existence Result via Krasnoselskii's Fixed Point Theorem
217(3)
7.2.3 Existence Result via Leray-Schauder's Nonlinear Alternative
220(4)
7.2.4 Existence Result via Leray-Schauder's Degree Theory
224(2)
7.3 Langevin Inclusions Case
226(13)
7.3.1 The Lipschitz Case
226(4)
7.3.2 The Caratheodory Case
230(7)
7.3.3 The Lower Semicontinuous Case
237(1)
7.3.4 Examples
238(1)
7.4 Systems of Langevin equation
239(17)
7.5 Langevin Equations with Fractional Uncoupled Integral Conditions
256(5)
7.5.1 Existence Results for Uncoupled Case
257(4)
7.6 Notes and Remarks
261(2)
8 Boundary Value Problems for Impulsive Multi-Order Hadamard Fractional Differential Equations
263(34)
8.1 Introduction
263(1)
8.2 Boundary Value Problems for First Order Impulsive Multi-Order Hadamard Fractional Differential Equations
264(10)
8.3 On Caputo-Hadamard Type Fractional Impulsive Boundary Value Problems with Nonlinear Fractional Integral Conditions
274(21)
8.3.1 Existence Result via Krasnoselskii-Zabreiko's Fixed Point Theorem
278(6)
8.3.2 Existence Result via Sadovskii's Fixed Point Theorem
284(6)
8.3.3 Existence Result via O'Regan's Fixed Point Theorem
290(5)
8.4 Notes and Remarks
295(2)
9 IVP and BVP for Hybrid Hadamard Fractional Differential Equations and Inclusions
297(34)
9.1 Introduction
297(1)
9.2 IVPs for Hybrid Hadamard Fractional Differential Equations
297(5)
9.3 Fractional Hybrid Differential Inclusions of Hadamard Type
302(5)
9.4 BVP for Hybrid Fractional Differential Equations and Inclusions of Hadamard Type
307(6)
9.5 Boundary Value Problems for Fractional Hybrid Differential Inclusions
313(6)
9.6 Nonlocal BVPs for Hybrid Hadamard Fractional Differential Equations and Inclusions
319(11)
9.6.1 Existence Results: The Single Valued Case
319(5)
9.6.2 Existence Result: The Multivalued Case
324(6)
9.7 Notes and Remarks
330(1)
10 Positive Solutions for Hadamard Fractional Differential Equations on Infinite Domain
331(16)
10.1 Introduction
331(1)
10.2 Positive Solutions for Hadamard Fractional Differential Equations on Infinite Domain
331(1)
10.3 Auxiliary Results
332(8)
10.4 Existence of at Least Three Positive Solutions
340(4)
10.5 Existence of at Least One Positive Solution
344(2)
10.6 Notes and Remarks
346(1)
11 Fractional Integral Inequalities via Hadamard's Fractional Integral
347(56)
11.1 Introduction
347(1)
11.2 Hadamard Fractional Integral Inequalities
347(13)
11.3 On Mixed Type Riemann-Liouville and Hadamard Fractional Integral Inequalities
360(5)
11.4 Chebyshev Type Inequalities for Riemann-Liouville and Hadamard Fractional Integrals
365(14)
11.4.1 Applications
373(6)
11.5 Chebyshev Integral Inequalities via Hadamard's Fractional Integral
379(6)
11.5.1 Special Cases
384(1)
11.6 Integral Inequalities with "maxima"
385(16)
11.6.1 Useful Lemmas
386(1)
11.6.2 Main Results
387(9)
11.6.3 Applications to Hadamard Fractional Differential Equations with "maxima"
396(5)
11.7 Notes and Remarks
401(2)
References 403(10)
Index 413
Bashir Ahmad is a professor in the Department of Mathematics at King Abdulaziz University, and in 2009 he was awarded Best Researcher of King Abdulaziz University. His field of research is differential equations and applications, specifically in topics such as set-valued differential equations, functional differential equations, stability analysis, and fluid mechanics. Ahmed Alsaedi is an associate professor and the chairman of the Department of Mathematics at King Abdulaziz University.  Sotiris K. Ntouyas is professor emeritus in the Department of Mathematics at the University of Ioannina. He's published numerous books and articles throughout his career, including "Existence results for fractional order functional differential equations with infinite delay," which was awarded the "Top Cited Article 2005-2010" by the Journal of Mathematical Analysis & Applications.  Jessada Tariboon is a professor in theDepartment of Mathematics at King Mongkut's University of Technology. He is an editor for King Mongkut's Universty of Technology's International Journal of Applied Science and Technology. 
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97833195214112e.html
Märksõnad: