Analytical Solutions of the One-Dimensional Volterra Integro-Differential Equations within Local Fractional Derivative

Authors

  • Hassan Kamil Jassim Thi-Qar University
  • Ammar Ali Neamah University of Kufa

DOI:

https://doi.org/10.31642/JoKMC/2018/040106

Keywords:

Integral equations, Local fractional Volterra integro-differential equation, Local fractional variational iteration method, Local fractional operator, Analytical solutions

Abstract

The one-dimensional Volterra Integro-Differential Equations of the second kind associated with local fractional derivative operators are investigated. Analytical solutions are obtained by using the local fractional variational Iteration method (LFVIM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

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References

K. Kolwankar, A. D. Gangal, Local fractional Fokker Planck equation, Phys. Rev. Lett., vol. 80, pp.214- 217, 1998. DOI: https://doi.org/10.1103/PhysRevLett.80.214

J. H. He, A new fractal derivation, Thermal Science, vol.15, pp.145-147, 2011. DOI: https://doi.org/10.2298/TSCI11S1145H

J. H. He, S. K. Elagan, Z. B. Li, Geometrical explanation of the fractional complex and derivative chain rule for fractional calculus, Phy. Lett. A, vol.376, pp.257- 259, 2012. DOI: https://doi.org/10.1016/j.physleta.2011.11.030

A. Parvate, A. D. Gangal, Calculus on fractal subsets of real line I: formulation, Fractals, 17(1) (2009) 53-81. DOI: https://doi.org/10.1142/S0218348X09004181

A. Carpinteri, B. Cornetti, K. M. Kolwankar, Calculation of the tensile and flexural strength of disordered materials using fractional calculus, Chaos, Solitons, Fractals, 21 (2004) 623 632. DOI: https://doi.org/10.1016/j.chaos.2003.12.081

X. J Yang, Local Fractional Integral Transforms, Progr. Nonlinear Sci.,vol. 4, pp. 1- 225, 2011.

X. J Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic publisher Limited, Hong Kong, 2011.

H. K. Jassim, C. Ünlü, S. P. Moshokoa, C. M. Khalique, Local Fractional Laplace Variational Iteration Method for Solving Diffusion andWave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering,vol.2015Article ID 309870, pp. 1- 9, 2015. DOI: https://doi.org/10.1155/2015/309870

X. J. Yang, Local fractional partial differential equations with fractal boundary problems, ACMA, vol.1, pp. 60-63, 2012.

X. J. Yang, Local fractional Kernel transform fractal space and its applications, ACMA, vol.1, pp. 86-93, 2012.

X. J. Yang, Local fractional variational iteration method and its algorithms, ACMA,

vol.1, pp. 139-145, 2012. DOI: https://doi.org/10.1016/j.clim.2012.09.002

] X. J. Yang, Local fractional integral equations and their applications, ACSA, vol.1, pp. 234- 239, 2012.

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Published

2017-03-30

How to Cite

Jassim, H. K., & Neamah, A. A. (2017). Analytical Solutions of the One-Dimensional Volterra Integro-Differential Equations within Local Fractional Derivative. Journal of Kufa for Mathematics and Computer, 4(1), 46–50. https://doi.org/10.31642/JoKMC/2018/040106

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