Explicit solution of fractional order atmosphere-soil-land plant carbon cycle system |
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| Institution: | 1. Harran University, Faculty of Arts and Sciences, Department of Mathematics, Sanliurfa 63290, Turkey;2. Harran University, Faculty of Education, Department of Mathematics and Science Education, Sanliurfa 63290, Turkey;1. Georges Lemaître Center for Earth and Climate Research (TECLIM/ELIC), Earth & Life Institute, UCLouvain;2. Universidade Nove de Julho, Informatics and Knowledge Management Graduate Program, Rua Vergueiro, 235/249, São Paulo, 01525-000, SP, Brazil;1. College of Industrial Engineering, South Tehran Branch, Islamic Azad University, Entezari Alley, Oskoui Alley, Choobi Bridge, Tehran, Iran;2. College of Industrial Engineering, South Tehran Branch, Islamic Azad University, Entezari Alley, Oskoui Alley, Choobi Bridge, Tehran, Iran;3. Industrial Engineering Department, University of Science and Culture, Tehran, Iran;4. Department of Industrial Engineering, KHATAM University, Tehran, Iran;1. Czech University of Life Sciences Prague, Faculty of Forestry and Wood Sciences, Kamýcká 129, Praha 6 - Suchdol, 165 00, Czech Republic;2. Department of Life Sciences and System Biology, University of Turin, via Accademia Albertina 13, 10123 Turin, Italy;3. Department of Ethology, Institute of Animal Science, P?átelství 815, 104 00 Praha 10-Uh?íněves, Czech Republic;1. UNESCO Chair on “Environment, Resources and Sustainable Development”, Department of Science and Technology, Parthenope University of Naples, via F. Petrarca 80 (80123) Naples, Italy;2. CoNISMa, Piazzale Flaminio 9, (00197) Rome, Italy;3. Ischia Marine Center - Villa Dohrn, Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, P.ta S. Pietro, Ischia, Naples, Italy |
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| Abstract: | In this paper, the dynamical behaviours and mathematics of the fractional order atmosphere-soil-land plant carbon cycle system involving the time dependent variable of carbon flux in atmosphere, the carbon flux of soil, and the carbon flux of animals and plants are qualitatively and numerically investigated. Explicit solutions in terms of the Mittag-Leffler functions to the terrestrial carbon cycle system around the equilibrium point are first time reported by applying Laplace transform of Caputo fractional derivative. The graphs of obtained solutions the time dependent variable of carbon flux in atmosphere, the carbon flux of soil and the carbon flux of animals and plants are plotted against each other. Explicit solutions to original system and stability of the fractional order linearized system around the equilibrium point are graphically compared as well. |
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