Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications.
Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems.
- Presents a simple and comprehensive understanding of the field of fractional-order systems
- Offers practical knowledge on the design of fractional-order systems for different applications
- Exposes users to possible new applications for fractional-order systems
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xi | |
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1 Continuous and discrete symmetry methods for fractional differential equations |
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1 | (36) |
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1 | (2) |
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1.2 Continuous and discrete symmetry for classical differential equations |
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3 | (11) |
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1.3 Continuous symmetry for fractional differential equation |
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14 | (16) |
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1.4 Discrete symmetry for fractional Harry Dym equation |
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30 | (3) |
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33 | (4) |
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33 | (4) |
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2 Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model |
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37 | (32) |
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37 | (5) |
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42 | (4) |
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46 | (6) |
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2.4 Series solution of the considered system (2.2) under normal Caputo derivative |
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52 | (6) |
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2.5 General series solution of the considered system (2.3) |
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58 | (11) |
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Declaration of competing interest |
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65 | (1) |
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65 | (4) |
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3 Spatial-fractional derivatives for fluid flow and transport phenomena |
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69 | (28) |
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69 | (1) |
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70 | (2) |
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3.3 Spatial-fractional mass conservation equation |
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72 | (3) |
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3.4 Fractional Navier-Stokes equation |
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75 | (1) |
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76 | (5) |
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3.6 Fractional models of flow in porous media |
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81 | (2) |
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3.7 Fractional natural gas equation |
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83 | (2) |
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3.8 Fractional multiphase flows in porous media |
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85 | (3) |
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3.9 Special cases of two-phase flow |
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88 | (3) |
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3.10 Fractional convection-diffusion equation |
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91 | (2) |
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93 | (4) |
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94 | (3) |
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4 On the hybrid fractional chaotic systems: a numerical approach |
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97 | (22) |
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97 | (1) |
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4.2 Preliminaries and notations |
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98 | (1) |
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4.3 Hybrid fractional chaotic models |
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99 | (7) |
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4.4 Numerical methods for solving hybrid fractional models |
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106 | (3) |
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4.5 Numerical simulations |
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109 | (5) |
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114 | (5) |
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Declaration of competing interest |
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116 | (1) |
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116 | (3) |
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5 Iterative processes with fractional derivatives |
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119 | (32) |
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119 | (2) |
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121 | (2) |
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5.3 Design and analysis of iterative methods using fractional derivatives |
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123 | (9) |
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5.4 Numerical analysis of the proposed methods |
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132 | (12) |
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144 | (7) |
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149 | (1) |
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149 | (2) |
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6 Design of fractional-order finite-time sliding mode controllers for quadrotor UAVs subjected to disturbances and uncertainties |
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151 | (28) |
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151 | (5) |
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156 | (1) |
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6.3 Quadrotor system dynamics |
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157 | (2) |
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6.4 Fractional-order SMC controllers for quadrotors |
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159 | (10) |
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6.5 Simulation results and discussion |
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169 | (5) |
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174 | (5) |
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176 | (3) |
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7 Performance evaluation of fractional character vector control applied for doubly fed induction generator operating in a network-connected wind power system |
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179 | (34) |
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179 | (3) |
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7.2 Variable-speed wind power system modeling |
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182 | (5) |
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7.3 Vector control scheme of DFIG using fractional-order PI controllers |
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187 | (4) |
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7.4 Design of FOPI controllers applied in the power and current regulation loops |
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191 | (10) |
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7.5 Numerical results and analysis |
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201 | (7) |
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208 | (5) |
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210 | (3) |
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8 Finite time synchronization of discontinuous fractional order Cohen-Grossberg memristive neural networks with discrete delays under sliding mode control strategies |
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213 | (36) |
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213 | (4) |
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217 | (9) |
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226 | (13) |
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239 | (5) |
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244 | (5) |
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244 | (1) |
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244 | (5) |
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9 Variable-order control systems: a steady-state error analysis |
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249 | (22) |
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249 | (1) |
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9.2 Variable-order operators |
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250 | (1) |
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251 | (8) |
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9.4 A method for numerical simulation |
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259 | (1) |
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260 | (6) |
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266 | (5) |
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268 | (3) |
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10 Theoretical study in conformal thermal antennas optimized by a fractional energy |
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271 | (22) |
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271 | (2) |
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273 | (3) |
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10.3 Thermal optimization approach |
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276 | (5) |
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281 | (3) |
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10.5 Conformal fractional energy |
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284 | (5) |
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289 | (4) |
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289 | (4) |
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11 Optimal design of fractional-order Butterworth filter with improved accuracy and stability margin |
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293 | (30) |
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293 | (7) |
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300 | (4) |
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11.3 Simulation results and discussion |
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304 | (11) |
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315 | (8) |
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317 | (6) |
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12 Pseudospectral methods for the Riesz space-fractional Schrodinger equation |
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323 | (32) |
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323 | (3) |
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12.2 Space-fractional couplers |
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326 | (1) |
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12.3 Gegenbauer polynomials and their properties |
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327 | (3) |
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330 | (7) |
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12.5 Numerical experiments |
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337 | (9) |
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12.6 Conclusion and discussion |
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346 | (9) |
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349 | (6) |
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13 Transmission line modeling by fractional and topological generalization of the telegrapher's equation |
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355 | (48) |
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13.1 Classical and fractional telegrapher's equations |
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355 | (9) |
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13.2 Reduction of fractional telegrapher's equations to special cases |
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364 | (2) |
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13.3 Transmission line model |
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366 | (7) |
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13.4 Transmission line in transient regime |
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373 | (9) |
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13.5 Transmission line in steady-state regime and its frequency characteristics |
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382 | (21) |
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394 | (5) |
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399 | (4) |
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14 System approach for the frequency analysis of a fractional-order acoustic tube: application for the resonator of the flute instrument |
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403 | (26) |
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403 | (2) |
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405 | (6) |
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14.3 Frequency response analysis |
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411 | (1) |
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412 | (3) |
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14.5 Frequency analysis of the system approach |
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415 | (10) |
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14.6 Conclusions and future work |
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425 | (4) |
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425 | (4) |
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15 Fractional-order dynamics to study neuronal function |
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429 | (28) |
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Antonio Coronel-Escamilla |
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429 | (2) |
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15.2 Fractional calculus definitions |
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431 | (4) |
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15.3 Fractional-order dynamics in neuroscience |
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435 | (14) |
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15.4 Discussions and conclusions |
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449 | (8) |
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451 | (6) |
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16 Modeling woody plant tissue using different fractional-order circuits |
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457 | (18) |
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457 | (5) |
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16.2 Woody cell structure |
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462 | (1) |
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16.3 Bio-impedance models overview |
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463 | (2) |
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465 | (3) |
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468 | (7) |
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469 | (1) |
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469 | (6) |
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17 Analog and digital implementation of fractional-order FitzHugh-Nagumo (FO-FHN) neuron model |
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475 | (30) |
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475 | (2) |
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17.2 Fractional-order FitzHugh-Nagumo (FO-FHN) neuron model |
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477 | (4) |
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17.3 Analog implementations of the FO-FHN neuron model |
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481 | (12) |
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17.4 FPAA implementation of FO-FHN neuron network |
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493 | (2) |
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17.5 FPGA implementation of FO-FHN neuron model |
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495 | (4) |
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499 | (6) |
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501 | (4) |
Index |
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505 | |
Ahmed G. Radwan (Senior member IEEE) is a Professor in the Engineering Mathematics Department, Cairo University, Egypt, and Acting Director of Research, Nile University, Egypt. He was the Former Director of Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. Dr. Radwan was a visiting Professor in Computational Electromagnetic Lab (CEL), Electrical and Computer Engineering department (ECE), McMaster University, Canada in the interval [ 2008 2009], then he was selected to be a part of the first foundation research teams to join KAUST (King Abdullah University of Science and Technology) during the interval [ 2009 -2011]. His research interests include interdisciplinary concepts between mathematics and engineering applications such as fractional-order systems, bifurcation, chaos, memristor, and encryption. Dr. Radwan received the Cairo University excellence award for research in the engineering sciences in 2016, the Abdul Hameed Shoman Award for Arab Researchers in basic sciences in 2015, the state achievements award for research in mathematical sciences in 2012, the Cairo University achievements award for research in the engineering sciences in 2013, and the best researcher awards Nile University 2015 & 2016.
Dr. Radwan has more than 200 papers, h-index 30, and more than 3000 citations based on Scopus database. He is the Co-inventor of Six US patents, author/Co-author of Seven international books as well as 15-chapter books in the highly ranked publishers such as Elsevier and Springer. He received many research grants as Principle Investigator (PI), CO-PI, or Consultant from different national/international organizations. He was Invited to be Lead/Guest Editors in Journal of Circuits, Systems and Signal Processing, and Journal of Mathematical Problems in Engineering, and Complexity. He organized many special sessions, serve as TPC (Technical Program Committee) in several international conferences. He was selected as a member of the first scientific council of Egyptian Young Academy of Sciences (EYAS) as well as in the first scientific council of the Egyptian Center for the Advancement of Science, Technology, and Innovation (ECASTI) to empower and encourage Egyptian young scientists in science and technology and build knowledge-based societies. Dr. Farooq Ahmad Khanday (M15, SM19) received M.Sc. (Gold Medalist), M. Phil. and Ph.D. Degrees from University of Kashmir in 2004 2010 and 2013 respectively. From June 2005 to Jan. 2009, he served as Assistant Professor on contractual basis at University of Kashmir, Department of Electronics and Instrumentation Technology. In 2009, he joined to Department of Higher Education J&K and Department of Electronics and Vocational Studies, Islamia College of Science and Commerce Srinagar, as Assistant Professor. From May 2010 to May 2022, he served as Assistant Professor in the Department of Electronics and Instrumentation Technology, University of Kashmir. From May 2022, he is associate professor in the Department of Electronics and Instrumentation Technology, University of Kashmir. His research interests include Neuromorphic Computing, Fractional-order Circuits, Low-power circuit Design, Nano-Electronics and Stochastic Computing. He is author or co-author of more than 150 publications in peer reviewed indexed International and National journals/conferences of repute including IEEE Transactions and Eleven book chapters. Besides he has authored a book on Nanoscale Electronic Devices and Their Applications in CRC Press (Taylor and Francis) and has Edited one book on Neuromorphic Computing and three books on Fractional-order Systems in Elsevier. In addition he has one patent on Portable Microcontroller-Based Impedance Meter For Biological Tissue Analysis (563600). He is featuring in Stanford University list of top 2% cited Scientists in the world. He is also listed among the world top 0.25% researchers in the field of Nanoelectronic Devices for the year 2024, according to ScholarGPS, California, USA. He has been the Management Committee (MC) Observer of the COST Action CA15225 (Fractional-order systems - analysis, synthesis and their importance for future design) of European Union and INSA visiting scientist fellow 2020-21. He is the Editor of PLOS ONE journal. He is the senior member of IEEE and member of other professional societies. He is serving as a reviewer for many International and National scientific journals in Electronics. He has successfully guided many Ph.D., M. Phil scholars, and M. Tech thesis. Dr. Khanday also has completed/ongoing funded research projects to his credit and has established laboratories with state of the art facilities for pursuing research in the fields of IC design, Nanoelectronics, fractional-order systems, etc.
Lobna A. Said is a full-time Assistant Professor at the Faculty of Engineering and Applied Science and the Nano-Electronics Integrated System Research Center (NISC), Nile University (NU). She received the B.Sc. , the M.Sc., and the Ph.D. degrees in electronics and communications from Cairo University, Egypt, in 2007, 2011, and 2016, respectively. She has H-index 15, and more than 660 citations based on the Scopus database. She has over 85 publications distributed between high-impact journals, conferences, and book chapters. She was involved in many research grants as a Senior Researcher, or as a Co-PI from different national organizations. Her research interests are interdisciplinary, including system modeling, control techniques, optimization techniques, analog and digital integrated circuits, fractional-order circuits and systems, non-linear analysis, and chaos theory. She has received the Recognized Reviewer Award from many international journals. She is the Vice-Chair of research activities at the IEEE Computational Intelligence Egypt Chapter. She has received the Excellence Award from the Center for the Development of Higher education and Research in 2016. She is the Winner of Dr. Hazem Ezzat Prize for the outstanding researcher, NU 2019. She is one of the top 10 researchers at NU for the year 2018-2019. Recently, she was selected as a member of the Egyptian Young Academy of Sciences (EYAS) to empower and encourage young Egyptian scientists in science and technology and build knowledge-based societies. In 2020, she was selected to be an affiliate member of the African Academy of Science (AAS). She is in the technical program committee for many International Conferences.