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E-raamat: Integral Transforms and Engineering: Theory, Methods, and Applications [Taylor & Francis e-raamat]

, (University of the Free State)
  • Formaat: 454 pages, 180 Line drawings, black and white; 180 Illustrations, black and white
  • Sari: Mathematics and its Applications
  • Ilmumisaeg: 19-Apr-2023
  • Kirjastus: CRC Press
  • ISBN-13: 9781003359869
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  • Taylor & Francis e-raamat
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Integral Transforms and Engineering: Theory, Methods, and ApplicationsSuurem pilt
  • Formaat: 454 pages, 180 Line drawings, black and white; 180 Illustrations, black and white
  • Sari: Mathematics and its Applications
  • Ilmumisaeg: 19-Apr-2023
  • Kirjastus: CRC Press
  • ISBN-13: 9781003359869
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003359869
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.
Preface xv
Authors xvii
Chapter 1 Sumudu and Laplace Transforms
1(12)
1.1 Definitions
1(1)
1.2 Properties of Laplace and Sumudu transforms
2(11)
1.2.1 Properties of Laplace
3(1)
1.2.2 Properties of Sumudu
3(1)
1.2.3 Some examples of Sumudu and Laplace transforms
4(9)
Chapter 2 Transfer Functions and Diagrams
13(4)
Chapter 3 Analysis of First-order Circuit Model 1
17(10)
3.1 Analysis of first-order circuit model 1 with classical derivative
17(2)
3.2 Analysis of first-order circuit model 1 with Caputo ivative
19(2)
3.3 Analysis of first-order circuit model 1 with Caputo-Fabrizio derivative
21(2)
3.4 Analysis of first-order circuit model 1 with Atangana-Baleanu derivative
23(4)
Chapter 4 Analysis of First-order Circuit Model 2
27(10)
4.1 Analysis of first-order circuit model 2 with classical derivative
27(3)
4.2 Analysis of first-order circuit model 2 with Caputo derivative
30(2)
4.3 Analysis of first-order circuit model 2 with Caputo-Fabrizio derivative
32(2)
4.4 Analysis of first-order circuit model 2 with Atangana-Baleanu derivative
34(3)
Chapter 5 Analysis of Noninverting Integrators Model 1
37(8)
5.1 Analysis of Noninverting integrators model 1 with classical derivative
37(2)
5.2 Analysis of Noninverting integrators model 1 with Caputo derivative
39(1)
5.3 Analysis of Noninverting integrators model 1 with Caputo-Fabrizio derivative
40(2)
5.4 Analysis of Noninverting integrators model 1 with Atangana-Baleanu derivative
42(3)
Chapter 6 Analysis of Noninverting Integrators Model 2
45(8)
6.1 Analysis of Noninverting integrators model 2 with classical derivative
45(1)
6.2 Analysis of Noninverting integrators model 2 with Caputo derivative
46(2)
6.3 Analysis of Noninverting integrators model 2 with Caputo-Fabrizio derivative
48(1)
6.4 Analysis of Noninverting integrators model 2 with Atangana-Baleanu derivative
49(4)
Chapter 7 Analysis of Lag Network Model
53(10)
7.1 Analysis of lag network model with classical derivative
53(3)
7.2 Analysis of lag network model with Caputo derivative
56(1)
7.3 Analysis of lag network model with Caputo-Fabrizio derivative
57(2)
7.4 Analysis of lag network model with Atangana-Baleanu derivative
59(4)
Chapter 8 Analysis of Lead Network Model
63(10)
8.1 Analysis of Analysis of lead network model with classical derivative
63(2)
8.2 Analysis of lead network model with Caputo derivative
65(3)
8.3 Analysis of lead network model with Caputo-Fabrizio derivative
68(1)
8.4 Analysis of lead network model with Atangana-Baleanu derivative
69(4)
Chapter 9 Analysis of First-order Circuit Model 3
73(10)
9.1 Analysis of first-order circuit model 3 with classical derivative
73(2)
9.2 Analysis of first-order circuit model 3 with Caputo derivative
75(2)
9.3 Analysis of first-order circuit model 3 with Caputo-Fabrizio derivative
77(2)
9.4 Analysis of first-order circuit model 3 with Atangana-Baleanu derivative
79(4)
Chapter 10 Analysis of First-order Circuit Model 4
83(10)
10.1 Analysis of first-order circuit model 4 with classical derivative
83(2)
10.2 Analysis of first-order circuit model 4 with Caputo derivative
85(3)
10.3 Analysis of first-order circuit model 4 with Caputo-Fabrizio derivative
88(1)
10.4 Analysis of first-order circuit model 4 with Atangana-Baleanu derivative
89(4)
Chapter 11 Analysis of First-order Circuit Model 5
93(10)
11.1 Analysis of first-order circuit model 5 with classical derivative
93(2)
11.2 Analysis of first-order circuit model 5 with Caputo derivative
95(2)
11.3 Analysis of first-order circuit model 5 with Caputo-Fabrizio derivative
97(2)
11.4 Analysis of first-order circuit model 5 with Atangana-Baleanu derivative
99(4)
Chapter 12 Analysis of a Series RLC Circuit Model
103(10)
12.1 Analysis of a series RLC Circuit model with classical derivative
103(3)
12.2 Analysis of a series RLC Circuit model with Caputo derivative
106(1)
12.3 Analysis of a series RLC Circuit model with Caputo-Fabrizio derivative
107(2)
12.4 Analysis of a series RLC Circuit model with Atangana-Baleanu derivative
109(4)
Chapter 13 Analysis of a Parallel RLC Circuit Model
113(10)
13.1 Analysis of a parallel RLC circuit model with classical derivative
113(3)
13.2 Analysis of a parallel RLC circuit model with Caputo derivative
116(1)
13.3 Analysis of a parallel RLC circuit model with Caputo-Fabrizio derivative
117(3)
13.4 Analysis of a parallel RLC circuit model with Atangana-Baleanu derivative
120(3)
Chapter 14 Analysis of Higher Order Circuit Model 1
123(12)
14.1 Analysis of higher order circuit model 1 with classical derivative
123(2)
14.2 Analysis of higher order circuit model 1 with Caputo derivative
125(3)
14.3 Analysis of higher order circuit model 1 with Caputo-Fabrizio derivative
128(2)
14.4 Analysis of higher order circuit model 1 with Atangana-Baleanu derivative
130(5)
Chapter 15 Analysis of Higher Order Circuit Model 2
135(12)
15.1 Analysis of higher order circuit model 2 with classical derivative
135(2)
15.2 Analysis of higher order circuit model 2 with Caputo derivative
137(3)
15.3 Analysis of higher order circuit model 2 with Caputo-Fabrizio derivative
140(2)
15.4 Analysis of higher order circuit model 2 with Atangana-Baleanu derivative
142(5)
Chapter 16 Analysis of Higher Order Circuit Model 3
147(12)
16.1 Analysis of higher order circuit model 3 with classical derivative
147(2)
16.2 Analysis of higher order circuit model 3 with Caputo derivative
149(3)
16.3 Analysis of higher order circuit model 3 with Cputo-Fabrizio derivative
152(3)
16.4 Analysis of higher order circuit model 3 with Atangana-Baleanu derivative
155(4)
Chapter 17 Nonlinear Model 1
159(8)
Chapter 18 Chua Circuit Model
167(10)
Chapter 19 Applications of the Circuit Problems
177(8)
19.1 First problem
177(1)
19.2 Second problem
178(1)
19.3 Third problem
179(1)
19.4 Fourth problem
179(1)
19.5 Fifth problem
180(2)
19.6 Sixth problem
182(1)
19.7 Seventh problem
183(2)
Chapter 20 Existence and Uniqueness of the Solution
185(18)
20.1 First problem
185(3)
20.2 Second problem
188(1)
20.3 Third problem
189(3)
20.4 Fourth problem
192(2)
20.5 Fifth problem
194(3)
20.6 Sixth problem
197(2)
20.7 Seventh problem
199(4)
Chapter 21 Non-Linear Stochastic RLC Systems
203(136)
Chapter 22 Numerical Simulations of Some Circuit Problems
339(6)
22.1 First problem
339(1)
22.2 Second problem
340(1)
22.3 Third problem
341(1)
22.4 Fourth problem
342(3)
Chapter 23 Applications of General Integral Transform
345(100)
23.1 General Integral transform
345(7)
23.1.1 Mohand transform
346(1)
23.1.2 Sawi transform
347(1)
23.1.3 Elzaki transform
347(1)
23.1.4 Aboodh transform
348(1)
23.1.5 Pourreza transform
349(1)
23.1.6 α integral Laplace transform
349(1)
23.1.7 Kamal transform
350(1)
23.1.8 G transform
351(1)
23.1.9 Natural transform
351(1)
23.2 Integral transforms of some fractional differential equations
352(2)
23.3 General transform of the Mittag-Leffler functions
354(12)
23.3.1 Aboodh transform
354(1)
23.3.2 Mohand transform
355(2)
23.3.3 Sawi transform
357(1)
23.3.4 Elzaki transform
358(1)
23.3.5 Kamal transform
359(2)
23.3.6 Pourreza transform
361(1)
23.3.7 α integral Laplace transform
362(1)
23.3.8 G transform
363(2)
23.3.9 Natural transform
365(1)
23.4 General transform of the equations
366(8)
23.4.1 Elzaki transform
366(1)
23.4.2 Aboodh transform
367(1)
23.4.3 Pourreza transform
368(1)
23.4.4 Mohand transform
369(1)
23.4.5 Sawi transform
370(1)
23.4.6 Kamal transform
371(1)
23.4.7 G-transform
372(1)
23.4.8 Natural transform
373(1)
23.5 Applications 1
374(10)
23.5.1 Elzaki transform
374(1)
23.5.2 Aboodh transform
375(1)
23.5.3 Pourreza transform
376(1)
23.5.4 Mohand transform
377(1)
23.5.5 Sawi transform
378(1)
23.5.6 Kamal transform
379(2)
23.5.7 G - transform
381(1)
23.5.8 Natural transform
382(1)
23.5.9 α integral Laplace transform
383(1)
23.6 Applications II
384(16)
23.6.1 Elzaki transform
384(1)
23.6.2 Aboodh transform
385(1)
23.6.3 Pourreza transform
385(1)
23.6.4 Mohand transform
386(1)
23.6.5 Sawi transform
386(1)
23.6.6 Kamal transform
387(1)
23.6.7 G-transform
387(1)
23.6.8 Natural transform
388(1)
23.6.9 α integral Laplace transform
388(1)
23.6.10 Applications III
389(1)
23.6.11 Elzaki transform
389(1)
23.6.12 Mohand transform
390(1)
23.6.13 Kamal transform
390(1)
23.6.14 Aboodh transform
391(1)
23.6.15 Sawi transform
392(1)
23.6.16 a-Integral Laplace transform
392(1)
23.6.17 G - transform
393(1)
23.6.18 Pourreza transform
394(1)
23.6.19 Natural transform
394(1)
23.6.20 Applications IV
395(1)
23.6.21 Elzaki transform
395(1)
23.6.22 Aboodh transform
396(1)
23.6.23 Pourreza transform
396(1)
23.6.24 Mohand transform
397(1)
23.6.25 Sawi transform
397(1)
23.6.26 Kamal transform
398(1)
23.6.27 G transform
398(1)
23.6.28 Natural transform
399(1)
23.6.29 α integral Laplace transform
399(1)
23.7 Application V
400(4)
23.7.1 Elzaki transform
400(1)
23.7.2 Aboodh transform
400(1)
23.7.3 Pourreza transform
401(1)
23.7.4 Mohand transform
401(1)
23.7.5 Sawi transform
402(1)
23.7.6 Kamal transform
402(1)
23.7.7 G transform
403(1)
23.7.8 Natural transform
403(1)
23.7.9 α integral Laplace transform
404(1)
23.8 Application VI
404(41)
23.8.1 Elzaki transform
404(1)
23.8.2 Aboodh transform
405(1)
23.8.3 Pourreza transform
405(1)
23.8.4 Mohand transform
406(1)
23.8.5 Sawi transform
406(1)
23.8.6 Kamal transform
407(1)
23.8.7 G transform
407(1)
23.8.8 Natural transform
408(1)
23.8.9 α integral Laplace transform
408(1)
23.8.10 Simulations
409(36)
References 445(6)
Index 451
Abdon Atangana received his Ph.D. in 2013 from the University of the Free State, Bloemfontein, South Africa, where, since 2017 he has been a full professor within the faculty of natural and agricultural science He was included in the 2019 (Maths), 2020 (Cross-field) and the 2021 (Maths) Clarivate Web of Science lists of the World's top 1% scientists, and he was awarded The World Academy of Sciences (TWAS) inaugural Mohammed A. Hamdan award for contributions to science in developing countries. In 2018 Atangana was elected as a member of the African Academy of Sciences and in 2021 a member of The World Academy of Sciences. He also ranked number one in the world in mathematics, number 186 in the world in all the fields, and number one in Africa in all the fields, according to the Stanford list of 2% single-year table. He was one of the first recipients of the Obada Award 2018. He published a paper that was ranked by Clarivate in 2017 as the most cited mathematics paper in the world. To date, the studies of Atangana are published in more than 401 papers, which have appeared in the most prestigious international peer-reviewed journals and in six books published by top international publishers. Abdon Atangana has supervised the works of 20 masters, 15 Ph.D. students, and 6 post-doctoral fellows and serves as the editor in several internationally accredited journals. He has also organized more than 25 special issues in top tiers journals and has been a plenary and invited speaker in more than 25 international conferences.

Ali Akgül is a full professor at Siirt University, Art and Science Department of Mathematics. He is head of the Mathematics Department and has made a big contribution to the fractional calculus and numerical methods. He has published more than 250 research papers in various journals and has participated as an invited speaker at many international conferences. Dr. Akgül has received many scientific awards and has been on the global list of Stanford Universitys best top 2% Scientists in various disciplines for 2020 and 2021. He received the Obada-Prize Young Distinguished Researchers in 2022.
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