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E-raamat: Boundary Value Problems For Fractional Differential Equations And Systems

(Gheorghe Asachi Technical Univ Of Iasi,romania), (Baylor Univ, Usa), (King Abdulaziz Univ, Saudi Arabia)
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This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann–Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years. In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.

Preface vii
Notations xv
Chapter 1 Preliminaries
1(8)
1.1 Fractional Integral and Fractional Derivatives
1(2)
1.2 Fixed Point Theorems
3(6)
Chapter 2 Riemann-Liouville Fractional Differential Equations with Nonlocal Boundary Conditions
9(88)
2.1 Singular Fractional Differential Equations with Parameters and Multi-Point Boundary Conditions
9(16)
2.1.1 Auxiliary results
10(6)
2.1.2 Existence of positive solutions
16(7)
2.1.3 Examples
23(2)
2.2 A Fractional Differential Equation with Integral Terms and Multi-Point Boundary Conditions
25(14)
2.2.1 Existence of nonnegative solutions
26(12)
2.2.2 An example
38(1)
2.3 Semipositone Singular Fractional Boundary Value Problems with Integral Boundary Conditions
39(14)
2.3.1 Preliminary results
40(3)
2.3.2 Existence and multiplicity of positive solutions
43(7)
2.3.3 An example
50(3)
2.4 Singular Fractional Differential Equations with General Integral Boundary Conditions
53(15)
2.4.1 Auxiliary results
54(4)
2.4.2 Existence of multiple positive solutions
58(6)
2.4.3 An example
64(4)
2.5 On a Singular Fractional Boundary Value Problem with Parameters
68(13)
2.5.1 Existence of positive solutions
69(8)
2.5.2 Some remarks on a related semipositone problem
77(1)
2.5.3 Examples
78(3)
2.6 A Singular Fractional Differential Equation with Integral Boundary Conditions
81(16)
2.6.1 Preliminary results
82(1)
2.6.2 Existence and multiplicity of positive solutions
83(9)
2.6.3 An example
92(5)
Chapter 3 Systems of Two Riemann-Liouville Fractional Differential Equations with Multi-Point Boundary Conditions
97(58)
3.1 Systems of Fractional Differential Equations with Uncoupled Multi-Point Boundary Conditions
97(20)
3.1.1 Auxiliary results
98(3)
3.1.2 Existence and multiplicity of positive solutions
101(16)
3.2 Systems of Fractional Differential Equations with Coupled Multi-Point Boundary Conditions
117(38)
3.2.1 Preliminary results
117(11)
3.2.2 Nonsingular nonlinearities
128(10)
3.2.3 Singular nonlinearities
138(13)
3.2.4 Examples
151(4)
Chapter 4 Systems of Two Riemann-Liouville Fractional Differential Equations with p-Laplacian Operators, Parameters and Multi-Point Boundary Conditions
155(78)
4.1 Systems of Fractional Differential Equations with Uncoupled Multi-Point Boundary Conditions
155(36)
4.1.1 Auxiliary results
156(3)
4.1.2 Existence of positive solutions
159(22)
4.1.3 Nonexistence of positive solutions
181(6)
4.1.4 An example
187(2)
4.1.5 A relation between two supremum limits
189(2)
4.2 Systems of Fractional Differential Equations with Coupled Multi-Point Boundary Conditions
191(42)
4.2.1 Preliminary results
192(4)
4.2.2 Existence of positive solutions
196(22)
4.2.3 Nonexistence of positive solutions
218(9)
4.2.4 An example
227(6)
Chapter 5 Systems of Three Riemann-Liouville Fractional Differential Equations with Parameters and Multi-Point Boundary Conditions
233(46)
5.1 Systems of Fractional Differential Equations with Uncoupled Multi-Point Boundary Conditions
233(46)
5.1.1 Auxiliary results
234(4)
5.1.2 Existence of positive solutions
238(28)
5.1.3 Nonexistence of positive solutions
266(6)
5.1.4 Examples
272(7)
Chapter 6 Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problems
279(76)
6.1 Riemann-Liouville Fractional Differential Equations with Nonlocal Boundary Conditions
279(14)
6.1.1 Preliminary results
280(1)
6.1.2 Existence of solutions
281(10)
6.1.3 Examples
291(2)
6.2 Systems of Riemann-Liouville Fractional Differential Equations with Uncoupled Boundary Conditions
293(23)
6.2.1 Auxiliary results
294(3)
6.2.2 Existence of solutions
297(16)
6.2.3 Examples
313(3)
6.3 Systems of Riemann-Liouville Fractional Differential Equations with Coupled Boundary Conditions
316(39)
6.3.1 Preliminary results
317(7)
6.3.2 Existence of solutions
324(26)
6.3.3 Examples
350(5)
Chapter 7 Existence of Solutions for Caputo Fractional Boundary Value Problems
355(84)
7.1 Sequential Caputo Fractional Differential Equations and Inclusions with Nonlocal Boundary Conditions
355(32)
7.1.1 Auxiliary results
357(3)
7.1.2 Existence of solutions for problem (7.1), (7.3)
360(14)
7.1.3 Existence of solutions for problem (7.2), (7.3)
374(11)
7.1.4 Examples
385(2)
7.2 Sequential Caputo Fractional Integro-Differential Systems with Coupled Integral Boundary Conditions
387(31)
7.2.1 Preliminary results
388(7)
7.2.2 Existence of solutions
395(21)
7.2.3 Examples
416(2)
7.3 Caputo Fractional Differential Systems with Coupled Nonlocal Boundary Conditions
418(21)
7.3.1 Auxiliary results
419(3)
7.3.2 Existence of solutions
422(14)
7.3.3 Examples
436(3)
Bibliography 439(8)
Index 447
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