AN EFFECTIVE COMPUTATIONAL SCHEME FOR SOLVING VARIOUS MATHEMATICAL FRACTIONAL DIFFERENTIAL MODELS VIA NON-DYADIC HAAR WAVELETS FRACTIONAL DIFFERENTIAL MODELS VIA NON-DYADIC HAAR WAVELETS
Article Sidebar
Main Article Content
Abstract
The Non-dyadic Haar wavelet (Haar scale-3) collocation approach is used in this article to generate numerical solutions of fractional differential equations. The nonlinear fractional ordinary differential equations are linearized using the Quasilinearisation technique. The Haar scale-3 wavelet approach works on transforming the set of differential calculations into a set of linear algebraic equations. The reliability of the numerical solution can be improved by raising the degree of resolution, and error analysis can be done. The numerical examples are solved to test the method's simplicity and flexibility. The outcomes of numerical examples are compatible with the exact solution and provide better results than previous results existing in literature. This means that the procedure used here is consistent, reliable, and convenient to use.
Downloads
Article Details
Transfer of Copyrights
- In the event of publication of the manuscript entitled [INSERT MANUSCRIPT TITLE AND REF NO.] in the Malaysian Journal of Science, I hereby transfer copyrights of the manuscript title, abstract and contents to the Malaysian Journal of Science and the Faculty of Science, University of Malaya (as the publisher) for the full legal term of copyright and any renewals thereof throughout the world in any format, and any media for communication.
Conditions of Publication
- I hereby state that this manuscript to be published is an original work, unpublished in any form prior and I have obtained the necessary permission for the reproduction (or am the owner) of any images, illustrations, tables, charts, figures, maps, photographs and other visual materials of whom the copyrights is owned by a third party.
- This manuscript contains no statements that are contradictory to the relevant local and international laws or that infringes on the rights of others.
- I agree to indemnify the Malaysian Journal of Science and the Faculty of Science, University of Malaya (as the publisher) in the event of any claims that arise in regards to the above conditions and assume full liability on the published manuscript.
Reviewer’s Responsibilities
- Reviewers must treat the manuscripts received for reviewing process as confidential. It must not be shown or discussed with others without the authorization from the editor of MJS.
- Reviewers assigned must not have conflicts of interest with respect to the original work, the authors of the article or the research funding.
- Reviewers should judge or evaluate the manuscripts objective as possible. The feedback from the reviewers should be express clearly with supporting arguments.
- If the assigned reviewer considers themselves not able to complete the review of the manuscript, they must communicate with the editor, so that the manuscript could be sent to another suitable reviewer.
Copyright: Rights of the Author(s)
- Effective 2007, it will become the policy of the Malaysian Journal of Science (published by the Faculty of Science, University of Malaya) to obtain copyrights of all manuscripts published. This is to facilitate:
- Protection against copyright infringement of the manuscript through copyright breaches or piracy.
- Timely handling of reproduction requests from authorized third parties that are addressed directly to the Faculty of Science, University of Malaya.
- As the author, you may publish the fore-mentioned manuscript, whole or any part thereof, provided acknowledgement regarding copyright notice and reference to first publication in the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers) are given. You may produce copies of your manuscript, whole or any part thereof, for teaching purposes or to be provided, on individual basis, to fellow researchers.
- You may include the fore-mentioned manuscript, whole or any part thereof, electronically on a secure network at your affiliated institution, provided acknowledgement regarding copyright notice and reference to first publication in the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers) are given.
- You may include the fore-mentioned manuscript, whole or any part thereof, on the World Wide Web, provided acknowledgement regarding copyright notice and reference to first publication in the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers) are given.
- In the event that your manuscript, whole or any part thereof, has been requested to be reproduced, for any purpose or in any form approved by the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers), you will be informed. It is requested that any changes to your contact details (especially e-mail addresses) are made known.
Copyright: Role and responsibility of the Author(s)
- In the event of the manuscript to be published in the Malaysian Journal of Science contains materials copyrighted to others prior, it is the responsibility of current author(s) to obtain written permission from the copyright owner or owners.
- This written permission should be submitted with the proof-copy of the manuscript to be published in the Malaysian Journal of Science
References
Almeida, R., & Bastos, N. R. O. (2016). A numerical method to solve higher-order fractional differential equations. Mediterranean Journal of Mathematics, 13(3), 1339–1352.
Amin, R., Shah, K., Asif, M., Khan, I., & Ullah, F. (2021). An efficient algorithm for numerical solution of fractional integrodifferential equations via Haar wavelet. Journal of Computational and Applied Mathematics, 381, 113028.
Arora, G., Kumar, R., & Kaur, H. (2020). Scale-3 Haar wavelet and Quasi-linearisation based hybrid technique for solution of coupled space-time fractional-Burgers’ equation. Pertanika Journal of Science & Technology, 28(2), 579–607.
Baleanu, D., & Shiri, B. (2018). Collocation methods for fractional differential equations involving non-singular kernel. Chaos, Soliton & Fractals, 116, 136–145.
Chen, Y., Yi, M., & Yu, C. (2012). Error analysis for numerical solution of fractional differential equation by Haar wavelets method. Journal of Computational Science, 3(5), 367–373.
Das, S. (2011). Functional fractional calculus. Springer.
Gowrisankar, A., & Uthayakumar, R. (2016). Fractional calculus on fractal interpolation for a sequence of data with countable iterated function system. Mediterranean Journal of Mathematics, 13(6), 3887–3906.
Kobra, R., & Mohsen, R. (2021). Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations. Applied Numerical Mathematics, 168, 221–234.
Kumar, R., & Bakhtawar, S. (2022). An improved algorithm based on Haar scale 3 wavelets for the numerical solution of Integro-differential equations. Mathematics in Engineering, Science & Aerospace (MESA), 13(2), 617–633.
Kumar, R., & Gupta, J. (2022). Numerical analysis of linear and non-linear dispersive equation using Haar scale-3 wavelet. Mathematics in Engineering, Science & Aerospace (MESA), 13(4), 993–1006.
Li, C., & Zeng, F. (2015). Numerical methods for fractional calculus. Chapman & Hall/CRC.
Miller, K. S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. Wiley.
Mittal, R. C., & Pandit, S. (2018a). New scale-3 Haar wavelets algorithm for numerical simulation of second order ordinary differential equations. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 89(4), 799–808.
Mittal, R. C., & Pandit, S. (2018b). Quasi-linearized scale-3 Haar wavelets-based algorithm for numerical simulation of fractional dynamical systems. Engineering Computations (Swansea, Wales), 35(5), 1907–1931.
Odibat, Z., & Momani, S. (2008). Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order. Chaos, Solitons & Fractals, 36(1), 167–174.
Oldham, K. B., & Spanier, J. (1974). The fractional calculus: Theory and applications of differentiation and integration to arbitrary order. Academic Press.
Podlubny, I. (1999). Fractional differential equations. Academic Press.
Saeed, U., & Rehman, M. U. (2013). Haar wavelet–Quasi-linearization technique for fractional nonlinear differential equations. Applied Mathematics and Computation, 220, 630–648.
Shah, F. A., Abass, R., & Debnath, L. (2017). Numerical solution of fractional differential equations using Haar wavelet operational matrix method. International Journal of Applied and Computational Mathematics, 3(3), 2423–2445.
Shah, K., Khan, Z. A., Ali, A., Amin, R., Khan, H., and Khan, A. (2022). Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative. Alexandria Engineering Journal, 59(5), 3221–3231.
Shiralashetti, S. C., & Deshi, A. B. (2016). Haar wavelet collocation method for solving Riccati and fractional Riccati differential equations. Bulletin of Mathematical Sciences and Applications, 17, 46–56.
Su, H., Chen, W., Li, C., & Chen, Y. (2012). Finite difference schemes for variable-order time fractional diffusion equation. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 22(04), 1250–1085.