Integral Transforms and Engineering : Theory, Methods, and Applications

With the aim to better understand nature, mathematical tools are being used nowadays in many different fields. The concept of integral transforms, in particular, has been found to be a useful mathematical tool for solving a variety of problems not only in mathematics, but also in various other branches of science, engineering, and technology.Integral Transforms and Engineering: Theory, Methods, and Applications presents a mathematical analysis of integral transforms and their applications. The book illustrates the possibility of obtaining transfer functions using different integral transforms, especially when mapping any function into the frequency domain. Various differential operators, models, and applications are included such as classical derivative, Caputo derivative, Caputo-Fabrizio derivative, and Atangana-Baleanu derivative.This book is a useful reference for practitioners, engineers, researchers, and graduate students in mathematics, applied sciences, engineering, and technology fields. Cover Half Title Title Page Copyright Page Dedication Contents Preface Authors Chapter 1: Sumudu and Laplace Transforms 1.1. Definitions 1.2. Properties of Laplace and Sumudu transforms 1.2.1. Properties of Laplace 1.2.2. Properties of Sumudu 1.2.3. Some examples of Sumudu and Laplace transforms Chapter 2: Transfer Functions and Diagrams Chapter 3: Analysis of First-order Circuit Model 1 3.1. Analysis of first-order circuit model 1 with classical derivative 3.2. Analysis of first-order circuit model 1 with Caputo derivative 3.3. Analysis of first-order circuit model 1 with Caputo-Fabrizio derivative 3.4. Analysis of first-order circuit model 1 with Atangana-Baleanu derivative Chapter 4: Analysis of First-order Circuit Model 2 4.1. Analysis of first-order circuit model 2 with classical derivative 4.2. Analysis of first-order circuit model 2 with Caputo derivative 4.3. Analysis of first-order circuit model 2 with Caputo-Fabrizio derivative 4.4. Analysis of first-order circuit model 2 with Atangana-Baleanu derivative Chapter 5: Analysis of Noninverting Integrators Model 1 5.1. Analysis of Noninverting integrators model 1 with classical derivative 5.2. Analysis of Noninverting integrators model 1 with Caputo derivative 5.3. Analysis of Noninverting integrators model 1 with Caputo-Fabrizio derivative 5.4. Analysis of Noninverting integrators model 1 with Atangana-Baleanu derivative Chapter 6: Analysis of Noninverting Integrators Model 2 6.1. Analysis of Noninverting integrators model 2 with classical derivative 6.2. Analysis of Noninverting integrators model 2 with Caputo derivative 6.3. Analysis of Noninverting integrators model 2 with Caputo-Fabrizio derivative 6.4. Analysis of Noninverting integrators model 2 with Atangana-Baleanu derivative Chapter 7: Analysis of Lag Network Model 7.1. Analysis of lag network model with classical derivative 7.2. Analysis of lag network model with Caputo derivative 7.3. Analysis of lag network model with Caputo-Fabrizio derivative 7.4. Analysis of lag network model with Atangana-Baleanu derivative Chapter 8: Analysis of Lead Network Model 8.1. Analysis of Analysis of lead network model with classical derivative 8.2. Analysis of lead network model with Caputo derivative 8.3. Analysis of lead network model with Caputo-Fabrizio derivative 8.4. Analysis of lead network model with Atangana-Baleanu derivative Chapter 9: Analysis of First-order Circuit Model 3 9.1. Analysis of first-order circuit model 3 with classical derivative 9.2. Analysis of first-order circuit model 3 with Caputo derivative 9.3. Analysis of first-order circuit model 3 with Caputo-Fabrizio derivative 9.4. Analysis of first-order circuit model 3 with Atangana-Baleanu derivative Chapter 10: Analysis of First-order Circuit Model 4 10.1. Analysis of first-order circuit model 4 with classical derivative 10.2. Analysis of first-order circuit model 4 with Caputo derivative 10.3. Analysis of first-order circuit model 4 with Caputo-Fabrizio derivative 10.4. Analysis of first-order circuit model 4 with Atangana-Baleanu derivative Chapter 11: Analysis of First-order Circuit Model 5 11.1. Analysis of first-order circuit model 5 with classical derivative 11.2. Analysis of first-order circuit model 5 with Caputo derivative 11.3. Analysis of first-order circuit model 5 with Caputo-Fabrizio derivative 11.4. Analysis of first-order circuit model 5 with Atangana-Baleanu derivative Chapter 12: Analysis of a Series RLC Circuit Model 12.1. Analysis of a series RLC Circuit model with classical derivative 12.2. Analysis of a series RLC Circuit model with Caputo derivative 12.3. Analysis of a series RLC Circuit model with Caputo-Fabrizio derivative 12.4. Analysis of a series RLC Circuit model with Atangana-Baleanu derivative Chapter 13: Analysis of a Parallel RLC Circuit Model 13.1. Analysis of a parallel RLC circuit model with classical derivative 13.2. Analysis of a parallel RLC circuit model with Caputo derivative 13.3. Analysis of a parallel RLC circuit model with Caputo-Fabrizio derivative 13.4. Analysis of a parallel RLC circuit model with Atangana-Baleanu derivative Chapter 14: Analysis of Higher Order Circuit Model 1 14.1. Analysis of higher order circuit model 1 with classical derivative 14.2. Analysis of higher order circuit model 1 with Caputo derivative 14.3. Analysis of higher order circuit model 1 with Caputo-Fabrizio derivative 14.4. Analysis of higher order circuit model 1 with Atangana-Baleanu derivative Chapter 15: Analysis of Higher Order Circuit Model 2 15.1. Analysis of higher order circuit model 2 with classical derivative 15.2. Analysis of higher order circuit model 2 with Caputo derivative 15.3. Analysis of higher order circuit model 2 with Caputo-Fabrizio derivative 15.4. Analysis of higher order circuit model 2 with Atangana-Baleanu derivative Chapter 16: Analysis of Higher Order Circuit Model 3 16.1. Analysis of higher order circuit model 3 with classical derivative 16.2. Analysis of higher order circuit model 3 with Caputo derivative 16.3. Analysis of higher order circuit model 3 with Cputo-Fabrizio derivative 16.4. Analysis of higher order circuit model 3 with Atangana-Baleanu derivative Chapter 17: Nonlinear Model 1 Chapter 18: Chua Circuit Model Chapter 19: Applications of the Circuit Problems 19.1. First problem 19.2. Second problem 19.3. Third problem 19.4. Fourth problem 19.5. Fifth problem 19.6. Sixth problem 19.7. Seventh problem Chapter 20: Existence and Uniqueness of the Solution 20.1. First problem 20.2. Second problem 20.3. Third problem 20.4. Fourth problem 20.5. Fifth problem 20.6. Sixth problem 20.7. Seventh problem Chapter 21: Non-Linear Stochastic RLC Systems Chapter 22: Numerical Simulations of Some Circuit Problems 22.1. First problem 22.2. Second problem 22.3. Third problem 22.4. Fourth problem Chapter 23: Applications of General Integral Transform 23.1. General Integral transform 23.1.1. Mohand transform 23.1.2. Sawi transform 23.1.3. Elzaki transform 23.1.4. Aboodh transform 23.1.5. Pourreza transform 23.1.6. a integral Laplace transform 23.1.7. Kamal transform 23.1.8. G transform 23.1.9. Natural transform 23.2. Integral transforms of some fractional differential equations 23.3. General transform of the Mittag-Leffler functions 23.3.1. Aboodh transform 23.3.2. Mohand transform 23.3.3. Sawi transform 23.3.4. Elzaki transform 23.3.5. Kamal transform 23.3.6. Pourreza transform 23.3.7. α integral Laplace transform 23.3.8. G transform 23.3.9. Natural transform 23.4. General transform of the equations 23.4.1. Elzaki transform 23.4.2. Aboodh transform 23.4.3. Pourreza transform 23.4.4. Mohand transform 23.4.5. Sawi transform 23.4.6. Kamal transform 23.4.7. G- transform 23.4.8. Natural transform 23.5. Applications I 23.5.1. Elzaki transform 23.5.2. Aboodh transform 23.5.3. Pourreza transform 23.5.4. Mohand transform 23.5.5. Sawi transform 23.5.6. Kamal transform 23.5.7. G- transform 23.5.8. Natural transform 23.5.9. α integral Laplace transform 23.6. Applications II 23.6.1. Elzaki transform 23.6.2. Aboodh transform 23.6.3. Pourreza transform 23.6.4. Mohand transform 23.6.5. Sawi transform 23.6.6. Kamal transform 23.6.7. G- transform 23.6.8. Natural transform 23.6.9. α integral Laplace transform 23.6.10. Applications III 23.6.11. Elzaki transform 23.6.12. Mohand transform 23.6.13. Kamal transform 23.6.14. Aboodh transform 23.6.15. Sawi transform 23.6.16. α-Integral Laplace transform 23.6.17. G- transform 23.6.18. Pourreza transform 23.6.19. Natural transform 23.6.20. Applications IV 23.6.21. Elzaki transform 23.6.22. Aboodh transform 23.6.23. Pourreza transform 23.6.24. Mohand transform 23.6.25. Sawi transform 23.6.26. Kamal transform 23.6.27. G transform 23.6.28. Natural transform 23.6.29. α integral Laplace transform 23.7. Application V 23.7.1. Elzaki transform 23.7.2. Aboodh transform 23.7.3. Pourreza transform 23.7.4. Mohand transform 23.7.5. Sawi transform 23.7.6. Kamal transform 23.7.7. G transform 23.7.8. Natural transform 23.7.9. α integral Laplace transform 23.8. Application VI 23.8.1. Elzaki transform 23.8.2. Aboodh transform 23.8.3. Pourreza transform 23.8.4. Mohand transform 23.8.5. Sawi transform 23.8.6. Kamal transform 23.8.7. G transform 23.8.8. Natural transform 23.8.9. α integral Laplace transform 23.8.10. Simulations References Index "Integral Transforms and Engineering: Theory, Methods, and Applications presents a mathematical analysis of integral transforms and their applications. The book illustrates the possibility of obtaining transfer functions using different integral transforms, especially when mapping any function into the frequency domain. Various differential operators, models, and applications are included such as classical derivative, Caputo derivative, Caputo-Fabrizio derivative, and Atangana-Baleanu derivative"-- Provided by publisher