Applied Mathematics and Fractional Calculus
In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbit...
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| Định dạng: | Online |
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| Ngôn ngữ: | Tiếng Anh |
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2022
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| Truy cập trực tuyến: | ONIX_20220916_9783036551487_106 |
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| _version_ | 1869526542906818560 |
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| collection | Directory of Open Access Books |
| description | In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia. |
| format | Online |
| id | doab-20.500.12854ir-92120 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| record_format | ojs |
| spelling | doab-20.500.12854ir-921202024-03-28T03:32:26Z Applied Mathematics and Fractional Calculus González, Francisco Martínez Kaabar, Mohammed K. A. condensing function approximate endpoint criterion quantum integro-difference BVP existence fractional Kadomtsev-Petviashvili system lie group analysis power series solutions convergence analysis conservation laws symmetry weighted fractional operators convex functions HHF type inequality fractional calculus Euler–Lagrange equation natural boundary conditions time delay MHD equations weak solution regularity criteria anisotropic Lorentz space Sonine kernel general fractional derivative of arbitrary order general fractional integral of arbitrary order first fundamental theorem of fractional calculus second fundamental theorem of fractional calculus ρ-Laplace variational iteration method ρ-Laplace decomposition method partial differential equation caputo operator fractional Fornberg–Whitham equation (FWE) Riemann–Liouville fractional difference operator boundary value problem discrete fractional calculus existence and uniqueness Ulam stability elastic beam problem tempered fractional derivative one-sided tempered fractional derivative bilateral tempered fractional derivative tempered riesz potential collocation method hermite cubic spline fractional burgers equation fractional differential equation fractional Dzhrbashyan–Nersesyan derivative degenerate evolution equation initial value problem initial boundary value problem partial Riemann–Liouville fractional integral Babenko’s approach Banach fixed point theorem Mittag–Leffler function gamma function nabla fractional difference separated boundary conditions Green’s function existence of solutions Caputo q-derivative singular sum fractional q-differential fixed point equations Riemann–Liouville q-integral Shehu transform Caputo fractional derivative Shehu decomposition method new iterative transform method fractional KdV equation approximate solutions Riemann–Liouville derivative concave operator fixed point theorem Gelfand problem order cone integral transform Atangana–Baleanu fractional derivative Aboodh transform iterative method φ-Hilfer fractional system with impulses semigroup theory nonlocal conditions optimal controls fractional derivatives fractional Prabhakar derivatives fractional differential equations fractional Sturm–Liouville problems eigenfunctions and eigenvalues Fredholm–Volterra integral Equations fractional derivative Bessel polynomials Caputo derivative collocation points Caputo–Fabrizio and Atangana-Baleanu operators time-fractional Kaup–Kupershmidt equation natural transform Adomian decomposition method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia. 2022-09-16T13:47:47Z 2022-09-16T13:47:47Z 2022 book ONIX_20220916_9783036551487_106 9783036551487 9783036551470 https://directory.doabooks.org/handle/20.500.12854/92120 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/pdfview/book/5997 https://mdpi.com/books/pdfview/book/5997 10.3390/books978-3-0365-5147-0 10.3390/books978-3-0365-5147-0 MDPI - Multidisciplinary Digital Publishing Institute 9783036551487 9783036551470 438 Basel open access |
| spellingShingle | condensing function approximate endpoint criterion quantum integro-difference BVP existence fractional Kadomtsev-Petviashvili system lie group analysis power series solutions convergence analysis conservation laws symmetry weighted fractional operators convex functions HHF type inequality fractional calculus Euler–Lagrange equation natural boundary conditions time delay MHD equations weak solution regularity criteria anisotropic Lorentz space Sonine kernel general fractional derivative of arbitrary order general fractional integral of arbitrary order first fundamental theorem of fractional calculus second fundamental theorem of fractional calculus ρ-Laplace variational iteration method ρ-Laplace decomposition method partial differential equation caputo operator fractional Fornberg–Whitham equation (FWE) Riemann–Liouville fractional difference operator boundary value problem discrete fractional calculus existence and uniqueness Ulam stability elastic beam problem tempered fractional derivative one-sided tempered fractional derivative bilateral tempered fractional derivative tempered riesz potential collocation method hermite cubic spline fractional burgers equation fractional differential equation fractional Dzhrbashyan–Nersesyan derivative degenerate evolution equation initial value problem initial boundary value problem partial Riemann–Liouville fractional integral Babenko’s approach Banach fixed point theorem Mittag–Leffler function gamma function nabla fractional difference separated boundary conditions Green’s function existence of solutions Caputo q-derivative singular sum fractional q-differential fixed point equations Riemann–Liouville q-integral Shehu transform Caputo fractional derivative Shehu decomposition method new iterative transform method fractional KdV equation approximate solutions Riemann–Liouville derivative concave operator fixed point theorem Gelfand problem order cone integral transform Atangana–Baleanu fractional derivative Aboodh transform iterative method φ-Hilfer fractional system with impulses semigroup theory nonlocal conditions optimal controls fractional derivatives fractional Prabhakar derivatives fractional differential equations fractional Sturm–Liouville problems eigenfunctions and eigenvalues Fredholm–Volterra integral Equations fractional derivative Bessel polynomials Caputo derivative collocation points Caputo–Fabrizio and Atangana-Baleanu operators time-fractional Kaup–Kupershmidt equation natural transform Adomian decomposition method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Applied Mathematics and Fractional Calculus |
| title | Applied Mathematics and Fractional Calculus |
| title_full | Applied Mathematics and Fractional Calculus |
| title_fullStr | Applied Mathematics and Fractional Calculus |
| title_full_unstemmed | Applied Mathematics and Fractional Calculus |
| title_short | Applied Mathematics and Fractional Calculus |
| title_sort | applied mathematics and fractional calculus |
| topic | condensing function approximate endpoint criterion quantum integro-difference BVP existence fractional Kadomtsev-Petviashvili system lie group analysis power series solutions convergence analysis conservation laws symmetry weighted fractional operators convex functions HHF type inequality fractional calculus Euler–Lagrange equation natural boundary conditions time delay MHD equations weak solution regularity criteria anisotropic Lorentz space Sonine kernel general fractional derivative of arbitrary order general fractional integral of arbitrary order first fundamental theorem of fractional calculus second fundamental theorem of fractional calculus ρ-Laplace variational iteration method ρ-Laplace decomposition method partial differential equation caputo operator fractional Fornberg–Whitham equation (FWE) Riemann–Liouville fractional difference operator boundary value problem discrete fractional calculus existence and uniqueness Ulam stability elastic beam problem tempered fractional derivative one-sided tempered fractional derivative bilateral tempered fractional derivative tempered riesz potential collocation method hermite cubic spline fractional burgers equation fractional differential equation fractional Dzhrbashyan–Nersesyan derivative degenerate evolution equation initial value problem initial boundary value problem partial Riemann–Liouville fractional integral Babenko’s approach Banach fixed point theorem Mittag–Leffler function gamma function nabla fractional difference separated boundary conditions Green’s function existence of solutions Caputo q-derivative singular sum fractional q-differential fixed point equations Riemann–Liouville q-integral Shehu transform Caputo fractional derivative Shehu decomposition method new iterative transform method fractional KdV equation approximate solutions Riemann–Liouville derivative concave operator fixed point theorem Gelfand problem order cone integral transform Atangana–Baleanu fractional derivative Aboodh transform iterative method φ-Hilfer fractional system with impulses semigroup theory nonlocal conditions optimal controls fractional derivatives fractional Prabhakar derivatives fractional differential equations fractional Sturm–Liouville problems eigenfunctions and eigenvalues Fredholm–Volterra integral Equations fractional derivative Bessel polynomials Caputo derivative collocation points Caputo–Fabrizio and Atangana-Baleanu operators time-fractional Kaup–Kupershmidt equation natural transform Adomian decomposition method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | condensing function approximate endpoint criterion quantum integro-difference BVP existence fractional Kadomtsev-Petviashvili system lie group analysis power series solutions convergence analysis conservation laws symmetry weighted fractional operators convex functions HHF type inequality fractional calculus Euler–Lagrange equation natural boundary conditions time delay MHD equations weak solution regularity criteria anisotropic Lorentz space Sonine kernel general fractional derivative of arbitrary order general fractional integral of arbitrary order first fundamental theorem of fractional calculus second fundamental theorem of fractional calculus ρ-Laplace variational iteration method ρ-Laplace decomposition method partial differential equation caputo operator fractional Fornberg–Whitham equation (FWE) Riemann–Liouville fractional difference operator boundary value problem discrete fractional calculus existence and uniqueness Ulam stability elastic beam problem tempered fractional derivative one-sided tempered fractional derivative bilateral tempered fractional derivative tempered riesz potential collocation method hermite cubic spline fractional burgers equation fractional differential equation fractional Dzhrbashyan–Nersesyan derivative degenerate evolution equation initial value problem initial boundary value problem partial Riemann–Liouville fractional integral Babenko’s approach Banach fixed point theorem Mittag–Leffler function gamma function nabla fractional difference separated boundary conditions Green’s function existence of solutions Caputo q-derivative singular sum fractional q-differential fixed point equations Riemann–Liouville q-integral Shehu transform Caputo fractional derivative Shehu decomposition method new iterative transform method fractional KdV equation approximate solutions Riemann–Liouville derivative concave operator fixed point theorem Gelfand problem order cone integral transform Atangana–Baleanu fractional derivative Aboodh transform iterative method φ-Hilfer fractional system with impulses semigroup theory nonlocal conditions optimal controls fractional derivatives fractional Prabhakar derivatives fractional differential equations fractional Sturm–Liouville problems eigenfunctions and eigenvalues Fredholm–Volterra integral Equations fractional derivative Bessel polynomials Caputo derivative collocation points Caputo–Fabrizio and Atangana-Baleanu operators time-fractional Kaup–Kupershmidt equation natural transform Adomian decomposition method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20220916_9783036551487_106 |