پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 380 |
| تعداد مقالات | 3,343 |
| تعداد مشاهده مقاله | 5,045,283 |
| تعداد دریافت فایل اصل مقاله | 3,444,284 |
Approximate methods for solving local fractional integral equations | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 1، شهریور 2017، صفحه 40-51 اصل مقاله (261.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2660 | ||
| نویسنده | ||
| Hassan Kamil Jassim* | ||
| Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq | ||
| چکیده | ||
| This paper presents new analytical approximate methods such as local fractional variational iteration method and local fractional decomposition method for a family of the linear and nonlinear integral equations of the second kind within local fractional derivative operators. Some examples are presented to illustrate the efficiency and accuracy of the proposed methods. The obtained results reveal that the proposed methods are very efficient and simple tools for solving local fractional integral equations. | ||
| کلیدواژه‌ها | ||
| Local fractional integral equations؛ Local fractional variational iteration method؛ Local fractional decomposition method؛ Analytical approximate solutions | ||
| مراجع | ||
|
[1] M. Rahman, Integral Equations and their Applications, WIT Press, Southamp-ton, Boston, (2007). [2] J. Wiley, Integral Equations, A Wily-Interscience publication, Canada, (1989). [3] K.M. Kolwankar and A.D. Gangal, Hlder exponents of irregular signals and local fractional derivatives, Pramana J. Phys., 48 (1997), 49-68. [4] K.M. Kolwankar, A.D. Gangal, Local fractional FokkerPlanck equation, Phys. Rev. Lett., 80 (1998) 214-217. [5] W. Chen, Timespace fabric underlying anomalous diffusion, Chaos, Solitons and Fractals, 28 (2006), 923-929. [6] W. Chen, X.D. Zhang and D. Korosak, Investigation on fractional and fractal derivative relaxation- oscillation models, Int. J. Nonlinear, Sci. Num., 11 (2010),3-9. [7] J.H. He, A new fractal derivation, Thermal Science, 15 (2011), 140-147. [8] J.H. He, S.K. Elagan and Z.B. Li, Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Phy. Lett.A, 376 (2012), 257-259. [9] A. Parvate and A. D. Gangal, Fractal differential equations and fractal time dynamical systems, Pramana J. Phys., 64 (2005) 389-409. [10] A. Parvate and A. D. Gangal, Calculus on fractal subsets of real line -I, Fractals,17 (2009), 53-81. [11] A. Carpinteri, B. Cornetti and K. M. Kolwankar, Calculation of the tensile and flexural strength of disordered materials using fractional calculus, Chaos, Solitons and Fractals, 21 (2004), 623-632. [12] A.V. Dyskin, Effective characteristics and stress concentration materials with self-similar microstructure, Int. J. Sol. Struct., 42 (2005), 477-502. [13] X. J. Yang, Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative,ArXiv:1106.3010v1, (2011). [14] F.B. Adda and J. Cresson, About non-differentiable functions, J. Math. Anal. Appl., 263 (2001) 721-737. [15] A. Babakhani and V.D. Gejji, On calculus of local fractional derivatives, J. Math. Anal. Appl., 270 (2002), 66-79. [16] X.R. Li, Fractional Calculus, Fractal Geometry, and Stochastic Processes, Ph.D. Thesis, University of Western Ontario (2003). [17] Y. Chen, Y. Yan and K. Zhang, On the local fractional derivative, J. Math. Anal. Appl., 362 (2010), 17-33. [18] T. Christoph, Further remarks on mixed fractional Brownian motion,, Appl. Math. Sci., 38 (2009), 1885-1901. [19] D. Baleanu, H. K. Jassim, M. Al Qurashi, Approximate Analytical Solutions of Goursat Problem within Local Fractional Operators, Journal of Nonlinear Science and Applications, 9 (2016) 4829-4837. [20] X.J Yang, Local Fractional Functional Analysis and Its Applications, Asian Aca-demic publisher Limited, Hong Kong (2011). [21] S. P. Yan, H. Jafari, and H. K. Jassim, Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 (2014), 1-7. [22] H. Jafari and H. K. Jassim, Local Fractional Variational Iteration Method for Nonlinear Partial Differential Equations within Local Fractional Operators, Ap-plications and Applied Mathematics, 10 (2015), 1055-1065. [23] S. Xu, X. Ling, Y. Zhao and H. K. Jassim, A Novel Schedule for Solving the Two-Dimensional Diffusion in Fractal Heat Transfer, Thermal Science, 19 (2015),99-103. [24] H. Jafari, H. K. Jassim, F. Tchier and D. Baleanu, On the Approximate Solu-tions of Local Fractional Differential Equations with Local Fractional Operator,Entropy, 18 (2016), 1-12. [25] X. J. Yang, D. Baleanu, and W. P. Zhong, Approximation solutions for diffusion equation on Cantor time-space, Proceeding of the Romanian Academy, 14 (2013),127-133. [26] Y. J. Yang, and S. Q. Wang and H. K. Jassim, Local Fractional Function De-composition Method for Solving Inhomogeneous Wave Equations with Local Frac-tional Derivative, Abstract and Applied Analysis, 2014 (2014), 1-7. [27] H. K. Jassim, C. Unlu, S. P. Moshokoa, C. M. Khalique, Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 (2015), 1-9. | ||
|
آمار تعداد مشاهده مقاله: 51 تعداد دریافت فایل اصل مقاله: 75 |
||