Fractional Integrals and Derivatives: "True" versus "False"
This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional op...
Gorde:
| Formatua: | Online |
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| Hizkuntza: | ingelesa |
| Argitaratua: |
MDPI - Multidisciplinary Digital Publishing Institute
2021
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| Gaiak: | |
| Sarrera elektronikoa: | ONIX_20210501_9783036504940_221 |
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| _version_ | 1863743299176628224 |
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| collection | Directory of Open Access Books |
| description | This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue. |
| format | Online |
| id | doab-20.500.12854ir-68475 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-684752024-03-28T03:32:26Z Fractional Integrals and Derivatives: "True" versus "False" Luchko, Yuri fractional derivatives fractional integrals fractional calculus fractional anti-derivatives fractional operators integral transforms convergent series fractional integral fractional derivative numerical approximation translation operator distributed lag time delay scaling dilation memory depreciation probability distribution fractional models fractional differentiation distributed time delay systems Volterra equation adsorption fractional differential equations numerical methods smoothness assumptions persistent memory initial values existence uniqueness Crank–Nicolson scheme weighted Shifted Grünwald–Letnikov approximation space fractional convection-diffusion model stability analysis convergence order Caputo–Fabrizio operator Atangana–Baleanu operator fractional falculus general fractional derivative general fractional integral Sonine condition fractional relaxation equation fractional diffusion equation Cauchy problem initial-boundary-value problem inverse problem fractional calculus operators special functions generalized hypergeometric functions integral transforms of special functions thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue. 2021-05-01T15:10:56Z 2021-05-01T15:10:56Z 2021 book ONIX_20210501_9783036504940_221 9783036504940 9783036504957 https://directory.doabooks.org/handle/20.500.12854/68475 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/pdfview/book/3494 https://mdpi.com/books/pdfview/book/3494 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-0494-0 10.3390/books978-3-0365-0494-0 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036504940 9783036504957 280 Basel, Switzerland open access |
| spellingShingle | fractional derivatives fractional integrals fractional calculus fractional anti-derivatives fractional operators integral transforms convergent series fractional integral fractional derivative numerical approximation translation operator distributed lag time delay scaling dilation memory depreciation probability distribution fractional models fractional differentiation distributed time delay systems Volterra equation adsorption fractional differential equations numerical methods smoothness assumptions persistent memory initial values existence uniqueness Crank–Nicolson scheme weighted Shifted Grünwald–Letnikov approximation space fractional convection-diffusion model stability analysis convergence order Caputo–Fabrizio operator Atangana–Baleanu operator fractional falculus general fractional derivative general fractional integral Sonine condition fractional relaxation equation fractional diffusion equation Cauchy problem initial-boundary-value problem inverse problem fractional calculus operators special functions generalized hypergeometric functions integral transforms of special functions thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Fractional Integrals and Derivatives: "True" versus "False" |
| title | Fractional Integrals and Derivatives: "True" versus "False" |
| title_full | Fractional Integrals and Derivatives: "True" versus "False" |
| title_fullStr | Fractional Integrals and Derivatives: "True" versus "False" |
| title_full_unstemmed | Fractional Integrals and Derivatives: "True" versus "False" |
| title_short | Fractional Integrals and Derivatives: "True" versus "False" |
| title_sort | fractional integrals and derivatives true versus false |
| topic | fractional derivatives fractional integrals fractional calculus fractional anti-derivatives fractional operators integral transforms convergent series fractional integral fractional derivative numerical approximation translation operator distributed lag time delay scaling dilation memory depreciation probability distribution fractional models fractional differentiation distributed time delay systems Volterra equation adsorption fractional differential equations numerical methods smoothness assumptions persistent memory initial values existence uniqueness Crank–Nicolson scheme weighted Shifted Grünwald–Letnikov approximation space fractional convection-diffusion model stability analysis convergence order Caputo–Fabrizio operator Atangana–Baleanu operator fractional falculus general fractional derivative general fractional integral Sonine condition fractional relaxation equation fractional diffusion equation Cauchy problem initial-boundary-value problem inverse problem fractional calculus operators special functions generalized hypergeometric functions integral transforms of special functions thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | fractional derivatives fractional integrals fractional calculus fractional anti-derivatives fractional operators integral transforms convergent series fractional integral fractional derivative numerical approximation translation operator distributed lag time delay scaling dilation memory depreciation probability distribution fractional models fractional differentiation distributed time delay systems Volterra equation adsorption fractional differential equations numerical methods smoothness assumptions persistent memory initial values existence uniqueness Crank–Nicolson scheme weighted Shifted Grünwald–Letnikov approximation space fractional convection-diffusion model stability analysis convergence order Caputo–Fabrizio operator Atangana–Baleanu operator fractional falculus general fractional derivative general fractional integral Sonine condition fractional relaxation equation fractional diffusion equation Cauchy problem initial-boundary-value problem inverse problem fractional calculus operators special functions generalized hypergeometric functions integral transforms of special functions thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20210501_9783036504940_221 |