Local fractional Sumudu transform with application to IVPs on cantor sets

Abstract and Applied Analysis

Volumn 2014, Issue , 2014, Pages

  Srivastava, H M ^a   Golmankhaneh, Alireza Khalili ^b   Baleanu, Dumitru ^c,d,e   Yang, Xiao Jun ^f  

^a UNIVERSITY OF VICTORIA   (Canada)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

^c KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^d INSTITUTE OF SPACE SCIENCES   (Romania)

^e CANKAYA UNIVERSITY   (Turkey)

^f CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84902192003     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2014/620529     Document Type: Article

References (37)

1. Mandelbrot B. B., The Fractal Geometry of Nature 1982 San Francisco, Calif, USA W. H. Freeman and Company MR665254
2. Falconer K., Fractal Geometry: Mathematical Foundations and Applications 1990 New York, NY, USA John Wiley & Sons MR1102677
3. Falconer K., Techniques in Fractal Geometry 1997 Chichester, UK John Wiley & Sons MR1449135
4. Edgar G. A., Integral, Probability, and Fractal Measures 1998 New York, NY, USA Springer 10.1007/978-1-4757-2958-0 MR1484412
5. Oldham K. B., Spanier J., The Fractional Calculus 1974 New York, NY, USA Academic Press MR0361633
6. Miller K. S., Ross B., An Introduction to the Fractional Integrals and Derivatives Theory and Applications 1993 New York, NY, USA John Wiley and Sons
7. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives Theory and Applications 1993 Yverdon, Switzerland Gordon and Breach Science MR1347689
8. Hilfer R., Applications of Fractional Calculus in Physics 2000 Singapore World Scientific 10.1142/9789812817747 MR1890104
9. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022
10. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science B.V. North-Holland Mathematics Studies MR2218073
11. Baleanu D., Diethelm K., Scalas E., Trujillo J. J., Fractional Calculus Models and Numerical Methods 2012 3 Hackensack, NJ, USA World Scientific Series on Complexity, Nonlinearity and Chaos 10.1142/9789814355216 MR2894576
12. Uchaikin V. V., Fractional Derivatives for Physicists and Engineers, Background and Theory 2013 Berlin, Germany Springer Nonlinear Physical Science MR3051754
13. West B. J., Bologna M., Grigolini P., Physics of Fractal Operators 2003 New York, NY, USA Springer Institute for Nonlinear Science 10.1007/978-0-387- 21746-8 MR1988873
14. Chen W., Sun H., Zhang X., Korošak D., Anomalous diffusion modeling by fractal and fractional derivatives. Computers & Mathematics with Applications 2010 59 5 1754 1758 10.1016/j.camwa.2009.08.020 MR2595948 ZBL1189.35355
15. Kolwankar K. M., Gangal A. D., Local fractional Fokker-Planck equation. Physical Review Letters 1998 80 2 214 217 10.1103/PhysRevLett.80.214 MR1604435 ZBL0945.82005 (Pubitemid 128621921)
16. Parvate A., Gangal A. D., Calculus on fractal subsets of real line. I. Formulation. Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society 2009 17 1 53 81 10.1142/S0218348X09004181 MR2498748 ZBL1173.28005
17. Parvate A., Satin S., Gangal A. D., Calculus on fractal curves in n. Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society 2011 19 1 15 27 10.1142/S0218348X1100518X MR2776738 ZBL1217.28014
18. Golmankhaneh A. K., Golmankhaneh A. K., Baleanu D., About Maxwell's equations on fractal subsets of R3. Central European Journal of Physics 2013 11 6 863 867
19. Golmankhaneh A. K., Fazlollahi V., Baleanu D., Newtonian mechanics on fractals subset of real-line. Romanian Reports in Physics 2013 65 1 84 93 2-s2.0-84877806817
20. Yang X.-J., Advanced Local Fractional Calculus and Its Applications 2012 New York, NY, USA World Science
21. Yang X.-J., Local Fractional Functional Analysis and Its Applications 2011 Hong Kong Asian Academic
22. Yang X.-J., Baleanu D., Tenreiro Machado J. A., Systems of Navier-Stokes equations on Cantor sets. Mathematical Problems in Engineering 2013 2013 8 769724 MR3070019 10.1155/2013/769724
23. Zhao Y., Baleanu D., Cattani C., Cheng D.-F., Yang X.-J., Maxwell's equations on Cantor sets: a local fractional approach. Advances in High Energy Physics 2013 2013 6 686371 MR3141419 10.1155/2013/686371
24. Yang X.-J., Baleanu D., Machado J. A. T., Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. Boundary Value Problems 2013 2013 131 10.1186/1687-2770-2013-131
25. Ma X.-J., Srivastava H. M., Baleanu D., Yang X.-J., A new Neumann series method for solving a family of local fractional Fredholm and Volterra integral equations. Mathematical Problems in Engineering 2013 2013 6 325121 MR3080049 10.1155/2013/325121
26. Baleanu D., Tenreiro Machado J. A., Cattani C., Baleanu M. C., Yang X.-J., Local fractional variational iteration and decomposition methods for wave equation on Cantor sets within local fractional operators. Abstract and Applied Analysis 2014 2014 6 535048 10.1155/2014/535048 MR3166628
27. He J.-H., Asymptotic methods for solitary solutions and compactons. Abstract and Applied Analysis 2012 2012 130 916793 MR2999914 ZBL1257.35158
28. Liu C. F., Kong S. S., Yuan S. J., Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem. Thermal Science 2013 17 3 715 721
29. Zhao C.-G., Yang A.-M., Jafari H., Haghbin A., The Yang-Laplace transform for solving the IVPs with local fractional derivative. Abstract and Applied Analysis 2014 2014 5 386459 10.1155/2014/386459 MR3166607
30. Wang S.-Q., Yang Y.-J., Jassim H. K., Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative. Abstract and Applied Analysis 2014 2014 7 176395 10.1155/2014/176395 MR3166575
31. Watugala G. K., Sumudu transform: a new integral transform to solve differential equations and control engineering problems. International Journal of Mathematical Education in Science and Technology 1993 24 1 35 43 10.1080/0020739930240105 MR1206847 ZBL0768.44003
32. Weerakoon S., Application of Sumudu transform to partial differential equations. International Journal of Mathematical Education in Science and Technology 1994 25 2 277 283 10.1080/0020739940250214 MR1271656 ZBL0812.35004
33. Deakin M. A. B., The Sumudu transform and the Laplace transform. International Journal of Mathematical Education in Science and Technology 1997 28 1 159 160
34. Asiru M. A., Sumudu transform and the solution of integral equations of convolution type. International Journal of Mathematical Education in Science and Technology 2001 32 6 906 910 10.1080/002073901317147870 MR1872543 ZBL1008.45003 (Pubitemid 33373503)
35. Aşiru M. A., Further properties of the Sumudu transform and its applications. International Journal of Mathematical Education in Science and Technology 2002 33 3 441 449 10.1080/002073902760047940 MR1912446 ZBL1013.44001
36. Eltayeb H., Kiliçman A., A note on the Sumudu transforms and differential equations. Applied Mathematical Sciences 2010 4 21-24 1089 1098 MR2607362 ZBL1207.34014
37. Belgacem F. B. M., Karaballi A. A., Kalla S. L., Analytical investigations of the Sumudu transform and applications to integral production equations. Mathematical Problems in Engineering 2003 3-4 103 118 10.1155/S1024123X03207018 MR2032184 (Pubitemid 38604138)