Fractional-Derivative Approximation of Relaxation in Complex Systems

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Model</td><td class="align_center"><span style="width: 6.50656ptpx;"><svg height="9.390339pt" id="M166" style="vertical-align:-3.429431pt" version="1.1" viewbox="-0.049816 -5.960908 6.50656 9.390339" width="6.50656pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g></svg></span></td><td class="align_center"><span style="width: 9.234718ptpx;"><svg height="9.142413pt" id="M167" style="vertical-align:-3.181505pt" version="1.1" viewbox="-0.049816 -5.960908 9.234718 9.142413" width="9.234718pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.189,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg></span></td><td class="align_center"><span style="width: 9.234718ptpx;"><svg height="9.142413pt" id="M168" 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177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">A</td><td class="align_center">1</td><td class="align_center">-2.4903</td><td class="align_center">0.8055</td><td class="align_center"><span style="width: 7.759248ptpx;"><svg height="7.354729pt" id="M171" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.049816 -7.004799 7.759248 7.354729" width="7.759248pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H52V230H535Z"></path></g></svg></span></td><td class="align_center">20</td></tr><tr><td class="align_left">B</td><td class="align_center">1.6708</td><td class="align_center">0.3313</td><td class="align_center">1.8067</td><td class="align_center">-0.1093</td><td class="align_center">6.94</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Model parameters from heat exchanger data.</div>

Complexity

tab1

Table 1

Table 1: Fractional-Derivative Approximation of Relaxation in Complex Systems 