Отправить статью по E-mail $\alpha$-Дифференцируемые функции в комплексной плоскости
- Авторы: Pashaei R.1, Pishkoo A.2, Asgari M.S.1, Ebrahimi Bagha D.1
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Учреждения:
- Islamic Azad University Central Tehran Branch
- Nuclear Science and Technology Research Institute
- Выпуск: Том 24, № 2 (2020)
- Страницы: 379-389
- Раздел: Статьи
- URL: https://bakhtiniada.ru/1991-8615/article/view/41995
- DOI: https://doi.org/10.14498/vsgtu1734
- ID: 41995
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Аннотация
В комплексной плоскости вводится взвешенная дробная производная порядка $\alpha$.Относительно многозначной функции $ z ^ {1- \alpha} $ получены дробные уравнения Коши–Римана, которые при $ \alpha = 1 $ совпадают с классическими уравнениями Коши–Римана.Для некоторых функций в комплексной плоскости рассмотрены свойства, относящиеся к комплексной взвешенной дробной производной.Обсуждаются два комплексных дифференциальных уравнения специальной формы. Для некоторых значений $\alpha$ приводятся римановы поверхности их решений и сравниваются их графики.
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Ronak Pashaei
Islamic Azad University Central Tehran Branch
Amir Pishkoo
Nuclear Science and Technology Research Institute
Email: apishkoo@gmail.com
Mohammad Sadegh Asgari
Islamic Azad University Central Tehran Branch
Email: msasgari@yahoo.com, moh.asgari@iauctb.ac.ir
Davood Ebrahimi Bagha
Islamic Azad University Central Tehran BranchPhD, профессор
Список литературы
- Tenreiro Machado J., Kiryakova V., Mainardi F., "A poster about the recent history of fractional calculus", Fract. Calc. Appl. Anal., 13:3 (2010), 329-334
- Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publ., Neq York, 1993, xxxvi+976 pp.
- Oldham K., Spanier J., The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, Mathematics in Science and Engineering, 111, Academic Press, New York, London, 1974, xiii+234 pp.
- de Oliveira E. C., Solved Exercises in Fractional Calculus, Studies in Systems, Decision and Control, 240, Springer, Cham, 2019, xviii+321 pp.
- Tenreiro Machado J., Kiryakova V., Mainardi F., "Recent history of fractional calculus", Comm. Nonlinear Science Numerical Simulation, 16:3 (2011), 1140-1153
- Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier, Amsterdam, 2006, xv+523 pp.
- Podlubny J., Fractional Differential Equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, 198, Academic Press, San Diego, CA, 1999, xxiv+340 pp.
- Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, 1993, xiii+366 pp.
- Pashaei R., Asgari M., Pishkoo A., "Conformable derivatives in Laplace equation and fractional Fourier series solution", Int. Ann. Sci., 9:1 (2019), 1-7
- Ortigueira M. D., Fractional Calculus for Scientists and Engineers, Lecture Notes in Electrical Engineering, 84, Springer, Dordrecht, 2011, xiv+152 pp.
- Khalil R., Al Horani M., Yousef A., Sababheh M., "A new definition of fractional derivative", J. Comp. Appl. Math., 264 (2014), 65-70
- Katugampola U. N., A new fractional derivative with classical properties, 2014
- Ortigueira M. D., Tenreiro Machado J. A., "What is a fractional derivative?", J. Comp. Phys., 293 (2015), 4-13
- Tarasov V. E., "No nonlocality. No fractional derivative", Commun. Nonlinear Sci. Numer. Simulat., 62 (2018), 157-163
- Tarasov V. E., "Electromagnetic fields on fractals", Modern Phys. Lett. A., 21:20 (2006), 1587-1600
- Li J., Ostoja-Starzewski M., "Fractal solids, product measures and fractional wave equations", Proc. R. Soc. A., 465:2108, 2521–2536
- Ostoja-Starzewski M., Li J., "Fractal materials, beams, and fracture mechanics", Z. angew. Math. Phys., 60:6 (2009), 1194-1205
- Ostoja-Starzewski M., "Electromagnetism on anisotropic fractal media", Z. angew. Math. Phys., 64:2 (2013), 381–390
- Ostoja-Starzewski M., Li J., Joumaa H., Demmie P. N., "From fractal media to continuum mechanics", Z. angew. Math. Mech., 94:5, 373-401
- Ortigueira M. D., Fractional Calculus for Scientists and Engineers, Lecture Notes in Electrical Engineering, 84, Springer, Dordrecht, 2011, xiv+154 pp.
- Olver P. J., Complex Analysis and Conformal Mapping, Lecture Notes, 2018, 84 pp.
- Abdeljawada T., Al-Mdallal Q. M., Jarad F., "Fractional logistic models in the frame of fractional operators generated by conformable derivatives", Chaos, Solitons and Fractals, 119 (2019), 94-101
- Ibrahim R. W., Meshram C., Hadid S. B., Momani S., "Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator", J. Ocean Eng. Sci., 5:2 (2020), 186-195
- Ebaid A., Masaedeh B., El-Zahar E., "A new fractional model for the falling body problem", Chinese Phys. Lett., 34:2, 020201
- Alharbi F.M., Baleanu D., Ebaid A., "Physical properties of the projectile motion using the conformable derivative", Chinese J. Phys., 58 (2019), 18-28
- Kaabar M.K.A., Novel methods for solving the conformable wave equation, 2019
- Chung W. S., "Fractional Newton mechanics with conformable fractional derivative", J. Comp. Appl. Math., 290 (2015), 150-158
- Morales-Delgado V. F., Gomez-Aguilar J. F., Taneco-Hernandez M. A., "Mathematical modeling approach to the fractional Bergman's model", Discrete Contin. Dyn. Syst. Ser. S, 13:3 (2020), 805-821
- C̨erdik Yaslan H., Mutlu F., "Numerical solution of the conformable differential equations via shifted Legendre polynomials", Int. J. Comp. Math., 97:5 (2020), 1016-1028
- Meng S., Cui Y., "The extremal solution to conformable fractional differential equations involving integral boundary condition", Mathematics, 7:2 (2019), 186
- Sibatov R. T., "Anomalous grain boundary diffusion: Fractional calculus approach", Adv. Math. Phys., 2019, 8017363, 9 pp.
- Alikhanov A. A., "A new difference scheme for the time fractional diffusion equation", J. Comp. Phys., 280 (2015), 424-438
- Amanov D., Ashyralyev A., "Initial-boundary value problem for fractional partial differential equations of higher order", Abstract and Applied Analysis, 2012, 973102, 16 pp.
- Application of Fractional Calculus in Physics, ed. R. Hilfer, World Scientific, Singapore, 2000
- Muslih S. I., Baleanu D., "Fractional multipoles in fractional space", Nonlinear Anal. RWA, 8:1 (2007), 198-203
- Tavazoei M. S., Haeri M., "Stabilization of unstable fixed points of chaotic fractional order systems by a state fractional PI controller", Eur. J. Control, 14:3 (2008), 247-257
- Ortigueira M. D., "A coherent approach to non-integer order derivatives", Signal Processing, 86:10 (2006), 2505-2515
- Li C., Dao X, Guoa P., "Fractional derivatives in complex planes", Nonlinear Analysis: Theory, Methods, Applications, 71:5-6 (2009), 1857-1869
- Owa S., "Some properties of fractional calculus operators for certain analytic functions", RIMS Kôkyûroku, 1626 (2009), 86-92
- Abdeljawad T., "On conformable fractional calculus", J. Comp. Appl. Math., 279 (2015), 57-66
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