Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers

<div>Exact solution of Example <a href="https://static.hindawi.com/articles/complexity/volume-2022/5630187/figures/#ex1">1</a> for <span class="nowrap"><svg height="11.5564pt" id="M324" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 85.1381 11.5564" width="85.1381pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><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,-0.013,16.05,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.586,0)"><path d="M501 444C501 643 409 712 321 712C208 712 108 618 108 502C108 412 172 331 293 331C337 331 394 359 420 378C397 154 341 41 258 41C209 41 178 76 178 161C178 232 171 299 114 299C76 299 38 272 23 257L29 232C42 236 54 239 66 239C91 239 106 221 102 149C95 20 158 -12 219 -12C264 -12 314 10 353 47C461 150 501 295 501 444ZM423 443C423 433 422 422 421 412C401 396 370 385 335 385C245 385 180 444 180 537C180 609 212 671 286 671C349 671 423 595 423 443Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.321,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.451,0)"><path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z"></path></g><g transform="matrix(.013,0,0,-0.013,51.947,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,56.432,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,62.672,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,67.815,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,74.055,0)"><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,-0.013,80.295,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg>.</span></div>

Complexity

fig2

Figure 2

Figure 2: Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers 

Figure 2 | Existence of a Unique Solution and the Hyers–Ulam-H-Fox Stability of the Conformable Fractional Differential Equation by Matrix-Valued Fuzzy Controllers 