New Challenges Arising in Engineering Problems with Fractional and Integer Order
Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all...
I tiakina i:
| Hōputu: | Online |
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| Reo: | Ingarihi |
| I whakaputaina: |
MDPI - Multidisciplinary Digital Publishing Institute
2022
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| Urunga tuihono: | ONIX_20220111_9783036519685_568 |
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Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
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| _version_ | 1869518729817096192 |
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| collection | Directory of Open Access Books |
| description | Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem. |
| format | Online |
| id | doab-20.500.12854ir-76833 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-768332024-04-09T23:16:33Z New Challenges Arising in Engineering Problems with Fractional and Integer Order Baskonus, Haci Mehmet Sánchez Ruiz, Luis Manuel Ciancio, Armando fractional kinetic equation Riemann–Liouville fractional integral operator incomplete I-functions Laplace transform fractional differential equations fractional generalized biologic population Sumudu transform Adomian decomposition method Caputo fractional derivative operator theory time scales integral inequalities Burgers’ equation reproducing kernel method error estimate Dirichlet and Neumann boundary conditions Caputo derivative Laplace transforms constant proportional Caputo derivative modeling Volterra-type fractional integro-differential equation Hilfer fractional derivative Lorenzo-Hartely function generalized Lauricella confluent hypergeometric function Elazki transform caputo fractional derivative predator–prey model harvesting rate stability analysis equilibrium point implicit discretization numerical scheme the (m + 1/G′)-expansion method the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation periodic and singular complex wave solutions traveling waves solutions chaotic finance fractional calculus Atangana-Baleanu derivative uniqueness of the solution fixed point theory shifted Legendre polynomials variable coefficient three-point boundary value problem modified alpha equation Bernoulli sub-equation function method rational function solution complex solution contour surface variable exponent fractional integral maximal operator n/a thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem. 2022-01-11T13:43:33Z 2022-01-11T13:43:33Z 2021 book ONIX_20220111_9783036519685_568 9783036519685 9783036519692 https://directory.doabooks.org/handle/20.500.12854/76833 eng image/jpeg Attribution 4.0 International https://mdpi.com/books/pdfview/book/4282 https://mdpi.com/books/pdfview/book/4282 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-1969-2 10.3390/books978-3-0365-1969-2 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036519685 9783036519692 182 Basel, Switzerland open access |
| spellingShingle | fractional kinetic equation Riemann–Liouville fractional integral operator incomplete I-functions Laplace transform fractional differential equations fractional generalized biologic population Sumudu transform Adomian decomposition method Caputo fractional derivative operator theory time scales integral inequalities Burgers’ equation reproducing kernel method error estimate Dirichlet and Neumann boundary conditions Caputo derivative Laplace transforms constant proportional Caputo derivative modeling Volterra-type fractional integro-differential equation Hilfer fractional derivative Lorenzo-Hartely function generalized Lauricella confluent hypergeometric function Elazki transform caputo fractional derivative predator–prey model harvesting rate stability analysis equilibrium point implicit discretization numerical scheme the (m + 1/G′)-expansion method the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation periodic and singular complex wave solutions traveling waves solutions chaotic finance fractional calculus Atangana-Baleanu derivative uniqueness of the solution fixed point theory shifted Legendre polynomials variable coefficient three-point boundary value problem modified alpha equation Bernoulli sub-equation function method rational function solution complex solution contour surface variable exponent fractional integral maximal operator n/a thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues New Challenges Arising in Engineering Problems with Fractional and Integer Order |
| title | New Challenges Arising in Engineering Problems with Fractional and Integer Order |
| title_full | New Challenges Arising in Engineering Problems with Fractional and Integer Order |
| title_fullStr | New Challenges Arising in Engineering Problems with Fractional and Integer Order |
| title_full_unstemmed | New Challenges Arising in Engineering Problems with Fractional and Integer Order |
| title_short | New Challenges Arising in Engineering Problems with Fractional and Integer Order |
| title_sort | new challenges arising in engineering problems with fractional and integer order |
| topic | fractional kinetic equation Riemann–Liouville fractional integral operator incomplete I-functions Laplace transform fractional differential equations fractional generalized biologic population Sumudu transform Adomian decomposition method Caputo fractional derivative operator theory time scales integral inequalities Burgers’ equation reproducing kernel method error estimate Dirichlet and Neumann boundary conditions Caputo derivative Laplace transforms constant proportional Caputo derivative modeling Volterra-type fractional integro-differential equation Hilfer fractional derivative Lorenzo-Hartely function generalized Lauricella confluent hypergeometric function Elazki transform caputo fractional derivative predator–prey model harvesting rate stability analysis equilibrium point implicit discretization numerical scheme the (m + 1/G′)-expansion method the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation periodic and singular complex wave solutions traveling waves solutions chaotic finance fractional calculus Atangana-Baleanu derivative uniqueness of the solution fixed point theory shifted Legendre polynomials variable coefficient three-point boundary value problem modified alpha equation Bernoulli sub-equation function method rational function solution complex solution contour surface variable exponent fractional integral maximal operator n/a thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues |
| topic_facet | fractional kinetic equation Riemann–Liouville fractional integral operator incomplete I-functions Laplace transform fractional differential equations fractional generalized biologic population Sumudu transform Adomian decomposition method Caputo fractional derivative operator theory time scales integral inequalities Burgers’ equation reproducing kernel method error estimate Dirichlet and Neumann boundary conditions Caputo derivative Laplace transforms constant proportional Caputo derivative modeling Volterra-type fractional integro-differential equation Hilfer fractional derivative Lorenzo-Hartely function generalized Lauricella confluent hypergeometric function Elazki transform caputo fractional derivative predator–prey model harvesting rate stability analysis equilibrium point implicit discretization numerical scheme the (m + 1/G′)-expansion method the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation periodic and singular complex wave solutions traveling waves solutions chaotic finance fractional calculus Atangana-Baleanu derivative uniqueness of the solution fixed point theory shifted Legendre polynomials variable coefficient three-point boundary value problem modified alpha equation Bernoulli sub-equation function method rational function solution complex solution contour surface variable exponent fractional integral maximal operator n/a thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues |
| url | ONIX_20220111_9783036519685_568 |