The Analysis of Fractional-Order Navier-Stokes Model Arising in the Unsteady Flow of a Viscous Fluid via Shehu Transform

<div>The first graph shows that the fractional-order of <svg height="8.55521pt" id="M231" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 39.2023 8.55521" width="39.2023pt" 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="M642 327C642 461 565 582 389 582C298 582 219 548 176 519L185 491C235 515 291 526 348 526C477 526 572 452 572 268C572 145 509 51 431 51C396 51 366 78 366 145C366 189 391 295 402 337L396 341L320 332C315 289 306 229 296 187C276 99 230 55 185 55C149 55 111 89 111 170C111 275 160 373 238 431L222 457C99 394 23 290 23 157C23 40 81 -12 142 -12C185 -12 254 33 293 86C301 31 340 -12 394 -12C437 -12 477 8 524 50C589 108 642 203 642 327Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.278,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.541,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.781,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.745,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g></svg> and the second graph shows that the fractional-order <svg height="8.55521pt" id="M232" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 39.2023 8.55521" width="39.2023pt" 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="M642 327C642 461 565 582 389 582C298 582 219 548 176 519L185 491C235 515 291 526 348 526C477 526 572 452 572 268C572 145 509 51 431 51C396 51 366 78 366 145C366 189 391 295 402 337L396 341L320 332C315 289 306 229 296 187C276 99 230 55 185 55C149 55 111 89 111 170C111 275 160 373 238 431L222 457C99 394 23 290 23 157C23 40 81 -12 142 -12C185 -12 254 33 293 86C301 31 340 -12 394 -12C437 -12 477 8 524 50C589 108 642 203 642 327Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.278,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.541,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.781,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.745,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g></svg> of Example 4.</div>

Journal of Function Spaces

fig11

Figure 11

Figure 11: The Analysis of Fractional-Order Navier-Stokes Model Arising in the Unsteady Flow of a Viscous Fluid via Shehu Transform 