Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.
In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Contributors - p. xi 7. Chapter 1: Fractional-order ordinary differential equations and properties - p. 1 8. Chapter 2: A numerical method for fractional-order differential equations from finance - p. 21 9. Chapter 3: Erdélyi–Kober fractional calculus due to contour integral representations related to double hypergeometric functions - p. 37 10. Chapter 4: Nonlinear fractional differential equation model analysis and application - p. 51 11. Chapter 5: On generalized Krätzel function and associated properties with applications - p. 67 12. Chapter 6: Effectiveness of the Kashuri–Fundo decomposition method in solving fractional differential equations - p. 79 13. Chapter 7: On a generalization of gamma function with applications in fractional calculus - p. 97 14. Chapter 8: Special functions in fractional calculus - p. 117 15. Chapter 9: Existence and uniqueness of the solution of Cauchy-type problem with Caputo derivative - p. 129 16. Chapter 10: Numerical evaluation of fractional derivative - p. 137 17. Chapter 11: Stability analysis of malware propagation in the computer network for fractional-order differential equations - p. 147 18. Chapter 12: Some inequalities for conformable fractional integrals by using a parameter - p. 159 19. Chapter 13: Fractional neutral functional q-differential equations - p. 179 20. Chapter 14: Approximate-analytical solutions to time-fractional diffusion equations - p. 199 21. Chapter 15: Fractional diffusion - p. 213 22. Chapter 16: Analysis of higher-order fractional integrodifferential equations using Caputo derivatives in RLC circuits - p. 239 23. Chapter 17: A comparative analysis on the optimal vaccination control for pneumococcal pneumonia infection - p. 251 24. Chapter 18: Biological application of fractal-fractional calculus - p. 261 25. Chapter 19: Solving boundary value problems for fractional differential equations by the method of separation of variables - p. 287 26. Chapter 20: The q-hypergeometric functions and associated integral transforms, generating functions, and their fractional calculus formulas - p. 301 27. Chapter 21: A new iterative method for solving generalized Caputo-type fractal-fractional differential equations - p. 313 28. Chapter 22: Solution of fractional kinetic equations by using Raizada polynomial - p. 323 29. Chapter 23: Solutions for a diffusion equation with nonlocal terms and geometric constraint - p. 333 30. Index - p. 347
Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.
In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Contributors - p. xi 7. Chapter 1: Fractional-order ordinary differential equations and properties - p. 1 8. Chapter 2: A numerical method for fractional-order differential equations from finance - p. 21 9. Chapter 3: Erdélyi–Kober fractional calculus due to contour integral representations related to double hypergeometric functions - p. 37 10. Chapter 4: Nonlinear fractional differential equation model analysis and application - p. 51 11. Chapter 5: On generalized Krätzel function and associated properties with applications - p. 67 12. Chapter 6: Effectiveness of the Kashuri–Fundo decomposition method in solving fractional differential equations - p. 79 13. Chapter 7: On a generalization of gamma function with applications in fractional calculus - p. 97 14. Chapter 8: Special functions in fractional calculus - p. 117 15. Chapter 9: Existence and uniqueness of the solution of Cauchy-type problem with Caputo derivative - p. 129 16. Chapter 10: Numerical evaluation of fractional derivative - p. 137 17. Chapter 11: Stability analysis of malware propagation in the computer network for fractional-order differential equations - p. 147 18. Chapter 12: Some inequalities for conformable fractional integrals by using a parameter - p. 159 19. Chapter 13: Fractional neutral functional q-differential equations - p. 179 20. Chapter 14: Approximate-analytical solutions to time-fractional diffusion equations - p. 199 21. Chapter 15: Fractional diffusion - p. 213 22. Chapter 16: Analysis of higher-order fractional integrodifferential equations using Caputo derivatives in RLC circuits - p. 239 23. Chapter 17: A comparative analysis on the optimal vaccination control for pneumococcal pneumonia infection - p. 251 24. Chapter 18: Biological application of fractal-fractional calculus - p. 261 25. Chapter 19: Solving boundary value problems for fractional differential equations by the method of separation of variables - p. 287 26. Chapter 20: The q-hypergeometric functions and associated integral transforms, generating functions, and their fractional calculus formulas - p. 301 27. Chapter 21: A new iterative method for solving generalized Caputo-type fractal-fractional differential equations - p. 313 28. Chapter 22: Solution of fractional kinetic equations by using Raizada polynomial - p. 323 29. Chapter 23: Solutions for a diffusion equation with nonlocal terms and geometric constraint - p. 333 30. Index - p. 347
