Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method

<div>A comparison of the exact solution and three terms’ approximate solution when <span class="nowrap"><svg height="11.1258pt" id="M151" style="vertical-align:-2.77698pt" version="1.1" viewbox="-0.0498162 -8.34882 67.892 11.1258" width="67.892pt" 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="M362 285L435 424L363 423C326 380 261 326 196 326C179 326 163 330 146 338L136 312C153 301 173 296 194 296C237 296 283 305 319 342L23 -209H100L241 53C356 266 508 411 595 411C620 411 631 395 631 371C631 279 519 97 461 65C440 69 423 69 404 69C348 69 314 44 314 21C314 4 335 -11 386 -11C417 -11 448 0 479 17C530 13 556 -8 603 -49L625 -29C598 7 560 30 520 46C613 110 694 248 694 342C694 417 646 441 602 441C535 441 460 395 365 283L362 285Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.681,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.944,0)"><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,-0.013,31.184,0)"><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,-0.013,36.327,0)"><path d="M725 202C666 143 457 -42 400 -103L397 -101L678 424H610L582 376H580C573 420 539 441 492 441C412 441 301 373 226 282C194 243 153 203 97 203C80 203 61 207 40 216L30 190C53 178 76 173 100 173C127 173 150 180 170 193C155 159 147 126 147 94C147 30 180 -11 231 -11C307 -11 367 26 438 102L440 101L271 -209H349C358 -198 419 -122 524 -25C628 70 702 141 743 184L725 202ZM550 364C550 260 376 19 246 19C223 19 205 33 205 60C205 96 228 156 291 247C367 358 440 406 496 406C525 406 550 397 550 364Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.099,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,61.362,0)"><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></svg>.</span></div>

Advances in Mathematical Physics

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Figure 1

Figure 1: Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method 