THERMAL SCIENCE

International Scientific Journal

Mustafa Bayram

,

Veysel Fuat Hatipoglu

,

Sertan Alkan

,

Sebahat Ebru Das

A SOLUTION METHOD FOR INTEGRO-DIFFERENTIAL EQUATIONS OF CONFORMABLE FRACTIONAL DERIVATIVE

ABSTRACT
The aim of this work is to determine an approximate solution of a fractional order Volterra-Fredholm integro-differential equation using by the Sinc-collocation method. Conformable derivative is considered for the fractional derivatives. Some numerical examples having exact solutions are approximately solved. The comparisons of the exact and the approximate solutions of the examples are presented both in tables and graphical forms.
KEYWORDS
Sinc-Collocation Method, Volterra-Fredholm integro-differential equation, Conformable fractional derivative
PAPER SUBMITTED: 2017-06-24
PAPER REVISED: 2017-11-14
PAPER ACCEPTED: 2017-11-18
PUBLISHED ONLINE: 2018-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI170624266B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S7 - S14]
REFERENCES
  1. Zhu, L., & Fan, Q.,Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW. Communications in Nonlinear Science and Numerical Simulation,(2013), 18(5), ID. 12031213.
  2. Saeedi, H., Moghadam, M. M., et. al. A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order. Communications in Nonlinear Science and Numerical Simulation, (2011), 16(3), pp:1154-1163.
  3. R.C. Mittal, Ruchi Nigam, Solution of fractional integro-differential equations by Adomian decomposition method, Int. J. Appl. Math. Mech., (2008), 4(2), pp:87-94.
  4. S. Momani, R. Qaralleh, An efficient method for solving systems of fractional integro-differential equations, Comput. Math. Appl., (2006), 52, pp:459-470.
  5. K. Sayevand, et. al., Convergence analysis of homotopy perturbation method for Volterra integrodifferential equations of fractional order, Alex. Eng. J., (2013), 52 (4), pp:807-812.
  6. F. Awawdeh, E.A. Rawashdeh, et. al. Analytic solution of fractional integro-differential equations, An. Univ. Craiova Ser. Mat. Inform., (2011), 38 (1), pp:1-10.
  7. M. Kurulay, A. Secer, Variational iteration method for solving nonlinear fractional integrodifferential equations, Int. J. Comput. Sci. Emer. Technol., (2011), 2 (1), pp:18-20.
  8. Khalil, R., Al Horani, et. al., A new definition of fractional derivative, J.Comput. Appl. Math. (2014), 264, pp:65-70.
  9. Thabet Abdeljawad, On the conformable fractional calculus, Journal of Computational and Applied Mathematics, (2015), 279, pp:57-66.
  10. I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
  11. A. Secer, S. Alkan , et. al. , Sinc-Galerkin method for approximate solutions of fractional order boundary value problems, Boundary Value Problems, (2013), 1, pp:1-14.
  12. S. Alkan, A. Secer, Application of Sinc-Galerkin Method for Solving Space-Fractional Boundary Value Problems, Mathematical Problems in Engineering, (2015), ID 217348.
  13. Khalil, R., Al Horani, et. al. A new definition of fractional derivative, J.Comput. Appl. Math., (2014), 264, pp:65-70.
  14. F. Stenger, Approximations via Whittaker's cardinal function, J. Approx. Theory, (1976), 17(3) ID.222240.
  15. S. Alkan, A. Secer, Solution of nonlinear fractional boundary value problems with nonhomogeneous boundary conditions, Appl. Comput. Math.,(2015), 14(3), pp:284-295.
  16. A. Atangana, On the new fractional derivative and application to nonlinear Fishers reactiondiffusion equation, Applied Mathematics and Computation,(2016), 273, pp:948-956.
  17. A. Atangana, D. Baleanu, A. Alsaedi, New properties of conformable derivative, Open Math.,(2015), 13(1), pp:889-898.
  18. S. Alkan, A new solution method for nonlinear fractional integro-differential equations, DCDS-S, (2015), 8(6), pp:1065-1077.
PDF VERSION [DOWNLOAD]
A solution method for integro-differential equations of conformable fractional derivative

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence