Conformable Dynamic Equations on Time Scales

✍ Scribed by Anderson, Douglas R.; Georgiev, Svetlin G

• Publisher: CRC Press LLC
• Year: 2020
• Tongue: English
• Leaves: 347
• Category: Library

✦ Synopsis

Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1: Conformable Dynamic Calculus on Time Scales -- 1.1 INTRODUCTION -- 1.2 CONFORMABLE DIFFERENTIATION -- 1.3 CONFORMABLE REGRESSIVE FUNCTIONS -- 1.4 THE CONFORMABLE EXPONENTIAL FUNCTION -- 1.5 CONFORMABLE HYPERBOLIC AND TRIGONOMETRIC FUNCTIONS -- 1.6 THE CONFORMABLE LOGARITHM FUNCTION -- 1.7 CONFORMABLE INTEGRATION -- 1.8 TAYLOR'S FORMULA -- 1.9 CALCULUS FOR THE NABLA CONFORMABLE DERIVATIVE -- 1.10 CONFORMABLE PARTIAL DERIVATIVES -- 1.11 ADVANCED PRACTICAL PROBLEMS -- 1.12 NOTES AND REFERENCES

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 10
1.1 INTRODUCTION......Page 12
1.2 CONFORMABLE DIFFERENTIATION......Page 13
1.3 CONFORMABLE REGRESSIVE FUNCTIONS......Page 28
1.4 THE CONFORMABLE EXPONENTIAL FUNCTION......Page 34
1.5 CONFORMABLE HYPERBOLIC AND TRIGONOMETRIC FUNCTIONS......Page 37
1.6 THE CONFORMABLE LOGARITHM FUNCTION......Page 42
1.7 CONFORMABLE INTEGRATION......Page 49
1.8 TAYLOR’S FORMULA......Page 56
1.9 CALCULUS FOR THE NABLA CONFORMABLE DERIVATIVE......Page 59
1.10 CONFORMABLE PARTIAL DERIVATIVES......Page 62
1.11 ADVANCED PRACTICAL PROBLEMS......Page 69
1.12 NOTES AND REFERENCES......Page 70
2.1 LINEAR FIRST-ORDER DYNAMIC EQUATIONS......Page 72
2.2 CONFORMABLE BERNOULLI EQUATIONS......Page 87
2.3 CONFORMABLE RICCATI EQUATIONS......Page 93
2.4 CONFORMABLE LOGISTIC EQUATIONS......Page 98
2.5 ADVANCED PRACTICAL PROBLEMS......Page 101
3.1 STRUCTURE OF CONFORMABLE DYNAMIC SYSTEMS ON TIME SCALES......Page 104
3.2 CONSTANT COEFFICIENTS......Page 135
3.3 ADVANCED PRACTICAL PROBLEMS......Page 148
4.1 CONFORMABLE GRONWALL INEQUALITY......Page 150
4.2 CONFORMABLE VOLTERRA-TYPE INTEGRAL INEQUALITIES......Page 159
4.3 CONFORMABLE INEQUALITIES OF GAMIDOV AND RODRIGUES......Page 164
4.4 SIMULTANEOUS CONFORMABLE INTEGRAL INEQUALITIES......Page 167
4.5 CONFORMABLE PACHPATTE’S INEQUALITIES......Page 168
4.6 A CONFORMABLE INTEGRO-DYNAMIC INEQUALITY......Page 173
5.1 EXISTENCE AND UNIQUENESS OF SOLUTIONS......Page 176
5.2 THE DEPENDENCY OF THE SOLUTION UPON THE INITIAL DATA......Page 180
5.3 LYAPUNOV FUNCTIONS......Page 181
5.4 BOUNDEDNESS OF SOLUTIONS......Page 183
5.5 EXPONENTIAL STABILITY......Page 189
5.6 ADVANCED PRACTICAL PROBLEMS......Page 194
6.1 HOMOGENEOUS HIGHER-ORDER LINEAR CONFORMABLE DYNAMIC EQUATIONS WITH CONSTANT COEFFICIENTS......Page 196
6.2 NONHOMOGENEOUS HIGHER-ORDER LINEAR CONFORMABLE DYNAMIC EQUATIONS WITH CONSTANT COEFFICIENTS......Page 201
6.3 ADVANCED PRACTICAL PROBLEMS......Page 205
7.1 HOMOGENEOUS SECOND-ORDER LINEAR CONFORMABLE DYNAMIC EQUATIONS......Page 208
7.2 REDUCTION OF ORDER......Page 223
7.3 METHOD OF FACTORING......Page 229
7.4 NONCONSTANT COEFFICIENTS......Page 236
7.5 CONFORMABLE EULER-CAUCHY EQUATIONS......Page 242
7.6 VARIATION OF PARAMETERS......Page 252
7.7 ADVANCED PRACTICAL PROBLEMS......Page 256
8.1 SELF-ADJOINT DYNAMIC EQUATIONS......Page 260
8.2 REDUCTION-OF-ORDER THEOREMS......Page 271
8.3 DOMINANT AND RECESSIVE SOLUTIONS......Page 273
8.4 RICCATI EQUATION......Page 284
8.5 CAUCHY FUNCTION AND VARIATION OF CONSTANTS FORMULA......Page 287
8.6 BOUNDARY VALUE PROBLEMS AND GREEN FUNCTIONS......Page 289
8.6.1 Conjugate Problem and Disconjugacy......Page 293
8.6.2 Right Focal Problem......Page 297
8.6.3 Periodic Problem......Page 299
9.1 DEFINITION AND PROPERTIES......Page 302
9.2 DECAY OF THE EXPONENTIAL FUNCTION......Page 310
9.3 CONVERGENCE OF THE CONFORMABLE LAPLACE TRANSFORM......Page 315
9.4 APPLICATIONS TO IVPS......Page 321
9.5 ADVANCED PRACTICAL PROBLEMS......Page 324
A.1 REMAINDERS......Page 326
A.2 DEFINITION AND UNIQUENESS OF THE FRE´CHET DERIVATIVE......Page 328
A.3 THE GATEAUX DERIVATIVE......Page 335
B.1 MEASURE CHAINS......Page 338
B.2 POTZSCHE’S CHAIN RULE......Page 340
Bibliography......Page 344
Index......Page 346

✦ Subjects

Difference equations;Differentiable dynamical systems;Electronic books