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Non-differentiable Solutions for Local Fractional Nonlinear Riccati Differential Equations

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFNRDE with constant coefficients is considered and non-differentiable solutions for special cases obtained.
Wydawca
Rocznik
Strony
409--417
Opis fizyczny
Bibliogr. 25 poz., wykr.
Twórcy
autor
  • School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China
  • Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
  • Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
autor
  • School of Computer Science and Technology, Nanjing Normal University, Nanjing 210023, Department of Mathematics and Mechanics, China
  • University of Mining and Technology, Xuzhou 221008, People’s Republic of China
Bibliografia
  • [1] Yang XJ, Baleanu D, Srivastava HM. Local fractional integral transforms and their applications, Elsevier/Academic Press, Amsterdam, 2016. ISBN-10: 0128040025, 13: 978-0128040027. doi: 10.1016/B978-0-12-804002-7.00001-2.
  • [2] Yang XJ, Srivastava HM. An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Communications in Nonlinear Science and Numerical Simulation, 2015; 29 (l): 499-504. doi: 10.1016/j.cnsns.2015.06.006.
  • [3] Yang XJ, Machado JAT. A new insight into complexity from the local fractional calculus view point: modelling growths of populations, Mathematical Methods in the Applied Sciences, in press, doi: 10.1002/mma.3765.
  • [4] Zhao D, Yang XJ, Srivastava HM. On the fractal heat transfer problems with local fractional calculus, Thermal Science, 2015; 19 (5): 1867-1871. doi: 10.2298/TSCI150821132Z.
  • [5] Yang XJ, Baleanu D, Srivastava HM. Local fractional similarity solution for the diffusion equation defined on Cantor sets, Applied Mathematics Letters, 2015; 47: 54-60. doi: 10.1016/j.am1.2015.02.024.
  • [6] Xu S, Ling X, Zhao Y, Jassim HK. A novel schedule for solving the two-dimensional diffusion problem in fractal heat transfer, Thermal Science, 2015; 19 (1): 99-103. doi: 10.2298/TSCI15S1S99X.
  • [7] Jafari H, Tajadodi H, Johnston JS. A decomposition method for solving diffusion equations via local fractional time derivative. Thermal Science, 2015; 19 (1): 123-129. doi: 10.2298/TSCI15S1S23J.
  • [8] Yan SP. Local fractional Laplace series expansion method for diffusion equation arising in fractal heat transfer, Thermal Science, 2015; 19 (1): 131-135. doi: 10.2298/TSCI141010063Y.
  • [9] Zhang Y, Srivastava HM, Baleanu MC. Local fractional variational iteration algorithm II for non- homogeneous model associated with the non-differentiable heat flow, Advances in Mechanical Engineering, 2015; 7 (10): 1-7. doi: 10.1177/1687814015608567.
  • [10] Jassim HK, Ünlü C, Moshokoa SP, Khalique CM. Local fractional Laplace variational iteration method for solving diffusion and wave equations on Cantor sets within local fractional operators, Mathematical Problems in Engineering, 2015: 1-9. doi: 10.1155/2015/309870.
  • [11] Baleanu D, Khan H, Jafari H, Khan RA. On the exact solution of wave equations on Cantor sets, Entropy. 2015; 17 (9): 6229-6237. doi: 10.3390/e17096229.
  • [12] Ahmad J, Mohyud-Din ST. Solving wave and diffusion equations on Cantor sets, Proceedings of the Pakistan Academy of Sciences, 2015; 52: 81-87. URL http://paspk.org/wp-content/uploads/proceedings/52,%20No.l/a4da22ebSolving%20Wave.pdf.
  • [13] Kƨlƨçman A, Saleh W. On geodesic strongly E-convex sets and geodesic strongly E-convex functions, Journal of Inequalities and Applications, 2015; 1: 1-10. doi: 10.1186/s13660-015-0824-z.
  • [14] Reid WT. Riccati differential equations, Academic Press, New York, 1972.
  • [15] Momani S, Shawagfeh N. Decomposition method for solving fractional Riccati differential equations. Applied Mathematics and Computation, 2006; 182 (2): 1083-1092. doi: 10.1016/j.amc.2006.05.008.
  • [16] Ortigueira MD, Machado JAT, Rivero M, Trujillo JJ. Integer/fractional decomposition of the impulse response of fractional linear systems, Signal Processing, 2015; 114: 85-88. doi: 10.1016/j.sigpro.2015.02.014.
  • [17] Almeida R, Pooseh S, Torres DFM. Computational methods in the fractional calculus of variations, Imperial College Press, London, 2015. doi: 10.1142/p991.
  • [18] Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier, Amsterdam, 2006.
  • [19] Yang X, Phillips P. Identification of green, Oolong and black teas in China via Wavelet Packet Entropy and Fuzzy Support Vector Machine, Entropy, 2015; 17 (10): 6663-6682. doi: 10.3390/e17106663.
  • [20] Zhang YD, Yang XJ, Cattani C, Rao RV. Tea Category Identification Using a Novel Fractional Fourer Entropy and Jaya Algorithm, Entropy, 2016; 18 (3): 77. doi: 10.3390/e18030077.
  • [21] Wang S, Zhang Y, Yang X, Sun P, Dong Z, Liu A, Yuan TF. Pathological Brain Detection by a Novel Image Feature - Fractional Fourier Entropy, Entropy, 2015; 17 (12): 8278-8296. doi: 10.3390/e17127877.
  • [22] Zhang Y, Wang S, Ji G, Phillips P. Fruit Classification using Computer Vision and Feedforward Neural Network, Journal of Food Engineering, 2014; 143: 167-177. doi: 10.1016/j.jfoodeng.2014.07.001.
  • [23] Wang S, Zhang Y, Ji G, Yang J, Wu J, Wei L. Fruit Classification by Wavelet-Entropy and Feedforward Neural Network trained by Fitness-scaled Chaotic ABC and Biogeography-based Optimization, Entropy, 2015; 17 (8): 5711-5728. doi: 10.3390/e17085711.
  • [24] Wang S, Zhang Y, Liu G, Phillips P, Yuan TF. Detection of Alzheimers Disease by Three-Dimensional Displacement Field Estimation in Structural Magnetic Resonance Imaging, Journal of Alzheimers Disease, 2016; 50 (l): 233-248. doi: 10.3233/JAD-150848.
  • [25] Zhang Y, Wang S, Phillips P, Yang J, Yuan TF. Three-dimensional eigenbrain for the detection of subjects and brain regions related with Alzheimers disease, Journal of Alzheimers Disease, 2016; 50 (4): 1163-1179. doi: 10.3233/JAD-150988.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b9f8d400-c4a5-4935-afeb-d7f454f3ab4b
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