THERMAL SCIENCE
International Scientific Journal
SIMULATION OF FRACTIONAL DIFFERENTIAL DIFFERENCE EQUATION VIA RESIDUAL POWER SERIES METHOD
ABSTRACT
In the present article, the fractional order differential difference equation is solved by using the residual power series method. Residual power series method solutions for classical and fractional order are obtained in a series form showing good accuracy of the method. Illustrative models are considered to affirm the legitimacy of the technique. The accuracy of the chosen problems is represented by tables and plots which show good accuracy between the exact and assimilated solutions of the models.
KEYWORDS
PAPER SUBMITTED: 2022-05-11
PAPER REVISED: 2022-05-24
PAPER ACCEPTED: 2022-06-01
PUBLISHED ONLINE: 2023-04-08
- Abd-Elhameed, W. M., Youssri, Y. H., Fifth-Kind Orthonormal Chebyshev Polynomial Solutions for Fractional Differential Equations, Computational and Applied Mathematics, 37 (2018). 3, pp. 2897- 2921
- Shah, R., et al., A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations, IEEE Access, 7 (2019), Oct., pp. 150037-150050
- Ullah, S., et al., A New Fractional Model for the Dynamics of the Hepatitis B Virus Using the Caputo-Fabrizio Derivative, The European Physical Journal Plus, 133 (2018), 6, 237
- Qureshi, S., Yusuf, A., Modelling Chickenpox Disease with Fractional Derivatives: From Caputo to Atangana-Baleanu, Chaos, Solitons and Fractals, 122 (2019), May, pp.111-118
- Qureshi, S., et al., Fractional Modelling of Blood Ethanol Concentration System with Real Data Application, Chaos: An Interdisciplinary Journal of Non-linear Science, 29 (2019), 1, 013143
- Liu, H., Lyapunov-Type Inequalities for Certain Higher-Order Difference Equations with Mixed Non-Linearities, Advances in Difference Equations, 2018 (2018), 229
- Khan, M. A., et al., A Fractional Order Pine Wilt Disease Model with Caputo-Fabrizio Derivative, Advances in Difference Equations, 1 (2018), 410
- Akinyemi, L., et al., Iterative Methods for Solving Fourth-and Sixth-Order Time-Fractional Cahn-Hillard Equation, Mathematical Methods in the Applied Sciences, 43 (2020), 7, pp. 4050-4074
- He, Y. A. N. G., Homotopy Analysis Method for the Time-Fractional Boussinesq Equation, Universal Journal of Mathematics and Applications, 3 (2020), 1, pp. 12-18
- He, J. H., Zhu, S. D., Differential-Difference Model for Nanotechnology, In Journal of Physics: Conference Series, 96 (2008), 1, 012189
- Baleanu, D., et al., A Central Difference Numerical Scheme for Fractional Optimal Control Problems, Journal of Vibration and Control, 15 (2009), 4, pp. 583-597
- Chen, B., et al., Applications of General Residual Power Series Method to Differential Equations with Variable Coefficients, Discrete Dynamics in Nature and Society, 2018 (2018), ID2394735
- El-Ajou, A., et al., New Results on Fractional Power Series: Theories and Applications, Entropy, 15 (2013), 12, pp. 5305-5323
- Alquran, M., Analytical Solutions of Fractional Foam Drainage Equation by Residual Power Series Method, Mathematical Sciences, 8 (2014), 4, pp. 153-160
- Prakash, J., et al., Numerical Approximations of Non-Linear Fractional Differential Difference Equations by Using Modified He-Laplace Method, Alexandria Engineering Journal, 55 (2016), 1, pp. 645-651
- Singh, M., Prajapati, R. N., Reliable Analysis for Time-Fractional Non-Linear Differential Difference Equations, Central European Journal of Engineering, 3 (2013), 4, pp. 690-699