A Modified Semi-Analytic Iterative Method for Solving a Class of Partial Integro-Differential Equations with Conformable Fractional Order Derivative
Keywords:
Partial Integro-Differential equations (PIDEs), Conformable fractional derivative, Shifted Legendre polynomials (SLPs)Abstract
In this paper, we introduce a modified semi analytic iterative method for solving conformable fractional Partial Integro-Differential equations (CFPIDEs). The methodology is tested by some illustrative examples which are given to demonstrate its accuracy, applicability and efficiency.
References
[1] Oldham, K.; Spanier, J.; "The fractional calculus theory and applications of differentiation and integration to arbitrary order"; Academic Press, New York, 1974.
[2] Podlubny, I.; "Fractional Differential Equations"; Academic Press, 1999.
[3] Atangana, A.; Secer, A.; "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions. Abstract and Applied Analysis"; 1-8, 2013.
[4] Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M.; "A new definition of fractional derivative, Computational and Applied Mathematics"; 65-70, 2014.
[5] Mohammed, D. S.; "Numerical solution of fractional integrodifferential equations by least squares method and shifted Chebyshev polynomial"; Math. Problems Eng. 5, 2014.
[6] El-Ajou, A.; Abu-Arqub, O.; Momani, S.; Baleanu, D.; Alsaedi, A.; "A novel expansion iterative method for solving linear partial differential equations of fractional order"; Appl. Math. Comput. 257, 119–133, 2015.
[7] Rostami, Y.; Maleknejad, K.; "Numerical solution of partial integro-differential equations by using projection method"; Mediter. J. Math. 14, 2017.
[8] Akilandeeswari, A.; Balachandran, K.; Rivero, M.; Trujillo, J. J. "On the solutions of partial integro-differential equations of fractional order"; 2017.
[9] Hamoud, A. A.; Ghadle, K. P.; "the approximate solutions of fractional volterra-fredholm integro-differential equations by using analytical Techniques"; Probl. Anal. Issues Anal. 7 (25), 41–58, 2018.
[10] Atangana, A.; Araz, S.; "Analysis of a new partial integro-differential equation with mixed fractional operators"; Chaos, Solitons and Fractals 127, 257–271, 2019.
[11] Hendi, F. A.; Al-Qarni, M. M.; "the variational Adomian decomposition method for solving nonlinear two- dimensional Volterra-Fredholm integro-differential equation" J. King Saud Univ. 31, 110–113, 2019.
[12] Ayşegül Daşcioğlu and Dilek Varol Bayram, "Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials"; Sains Malaysiana 48(1), 251–257, 2019.
[13] Abdeljawad, T.; "On conformable fractional calculus"; J. Comp. Appl. Math. 279, 57–66, 2015.
[14] Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; "A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equation"; Springer-Verlag Italia, 2015.
[15] Silva, F. S.; "Conformable Fractional Integral Equations of the Second Kind, Mathematica Aeterna"; vol. 8, 199-205, 2, 2,
[2] Podlubny, I.; "Fractional Differential Equations"; Academic Press, 1999.
[3] Atangana, A.; Secer, A.; "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions. Abstract and Applied Analysis"; 1-8, 2013.
[4] Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M.; "A new definition of fractional derivative, Computational and Applied Mathematics"; 65-70, 2014.
[5] Mohammed, D. S.; "Numerical solution of fractional integrodifferential equations by least squares method and shifted Chebyshev polynomial"; Math. Problems Eng. 5, 2014.
[6] El-Ajou, A.; Abu-Arqub, O.; Momani, S.; Baleanu, D.; Alsaedi, A.; "A novel expansion iterative method for solving linear partial differential equations of fractional order"; Appl. Math. Comput. 257, 119–133, 2015.
[7] Rostami, Y.; Maleknejad, K.; "Numerical solution of partial integro-differential equations by using projection method"; Mediter. J. Math. 14, 2017.
[8] Akilandeeswari, A.; Balachandran, K.; Rivero, M.; Trujillo, J. J. "On the solutions of partial integro-differential equations of fractional order"; 2017.
[9] Hamoud, A. A.; Ghadle, K. P.; "the approximate solutions of fractional volterra-fredholm integro-differential equations by using analytical Techniques"; Probl. Anal. Issues Anal. 7 (25), 41–58, 2018.
[10] Atangana, A.; Araz, S.; "Analysis of a new partial integro-differential equation with mixed fractional operators"; Chaos, Solitons and Fractals 127, 257–271, 2019.
[11] Hendi, F. A.; Al-Qarni, M. M.; "the variational Adomian decomposition method for solving nonlinear two- dimensional Volterra-Fredholm integro-differential equation" J. King Saud Univ. 31, 110–113, 2019.
[12] Ayşegül Daşcioğlu and Dilek Varol Bayram, "Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials"; Sains Malaysiana 48(1), 251–257, 2019.
[13] Abdeljawad, T.; "On conformable fractional calculus"; J. Comp. Appl. Math. 279, 57–66, 2015.
[14] Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; "A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equation"; Springer-Verlag Italia, 2015.
[15] Silva, F. S.; "Conformable Fractional Integral Equations of the Second Kind, Mathematica Aeterna"; vol. 8, 199-205, 2, 2,
Downloads
Published
2020-06-04
Issue
Section
Articles
How to Cite
[1]
“A Modified Semi-Analytic Iterative Method for Solving a Class of Partial Integro-Differential Equations with Conformable Fractional Order Derivative”, ANJS, vol. 23, no. 2, pp. 44–51, Jun. 2020, Accessed: Apr. 25, 2024. [Online]. Available: https://anjs.edu.iq/index.php/anjs/article/view/2277
.jpg)
