全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Natural Transform for Solving Fractional High Order Differential Equations

DOI: 10.4236/apm.2026.164018, PP. 341-350

Keywords: Natural Transform, Caputo Fractional Derivative, Fractional High Order Differential Equations, Analytical Solutions

Full-Text   Cite this paper   Add to My Lib

Abstract:

The natural transform (nt), a novel global method for solving fractional high-order differential equations (FDEs), is presented in this work. This technique functions as an all-encompassing integral transform that includes both Sumudu and Laplace transforms. Having inclusive fractional solutions for high-order fractional differential equations is the main goal of this work. The Caputo framework is used to express the fractional derivatives. To demonstrate the effectiveness, simplicity, and ease of use of the suggested approach and its applicability to the solution of differential equations in a variety of scientific domains, three problems are resolved.

References

[1]  Khan, Z.H. and Khan, W. (2008) N-Transform Properties and Applications. NUST Journal of Engineering Sciences, 1, 127-133.
[2]  Belgacem, F.B.M. and Silambarasan, R. (2012) Theory of Natural Transform. Mathematics in Engineering, Science and Aerospace, 3, 99-124.
[3]  Al-Omari, S.K.Q. (2013) On the Application of Natural Transforms. International Journal of Pure and Applied Mathematics, 85, 729-744.
https://doi.org/10.12732/ijpam.v85i4.9
[4]  Bulut, H., Baskonus, H.M. and Belgacem, F.B.M. (2013) The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method. Abstract and Applied Analysis, 2013, 1-6.
https://doi.org/10.1155/2013/203875
[5]  Loonker, D. and Banerji, P.K. (2013) Natural Transform for Distribution and Boehmian Spaces. Mathematics in Engineering, Science and Aerospace, 4, 69-76.
[6]  Loonker, D. and Banerji, P.K. (2014) Natural Transform and Solution of Integral Equations for Distribution Spaces. American Journal of Mathematics and Sciences, 3, 65-72.
[7]  Loonker, D. and Banerji, P.K. (2013) Applications of Natural Transform to Differential Equations. Journal of Indian Academic Mathematics, 35, 151-158.
[8]  Abdl-Rahim, H.R., Alharbi, S.A. and Ismail, G.M. (2025) Generalized Solutions of Fractional Burger’s Equation and Rational Physical Systems via a Neoteric Algorithm. Fractals, 9, 1-18.
https://doi.org/10.1142/s0218348x25402728
[9]  Abdl-Rahim, H.R., Alharbi, S.A. and Ismail, G.M. (2025) Analytical Study for Some Fractional Physical Models via Natural Transform Pade’ Approximation Method. Fractals, 9, 1-14.
https://doi.org/10.1142/s0218348x2540273x
[10]  Abdl-Rahim, H. (2024) Sumudu Transform Pade’ Approximation Method for Solving Fractional Physical Models. Sohag Journal of Sciences, 9, 167-173.
https://doi.org/10.21608/sjsci.2023.233564.1121
[11]  Abdl-Rahim, H.R., Ahmad, H., Nofal, T.A. and Ismail, G.M. (2023) Analytical and Approximate Solutions for Fractional Systems of Nonlinear Differential Equations. European Journal of Pure and Applied Mathematics, 16, 2632-2642.
https://doi.org/10.29020/nybg.ejpam.v16i4.4864
[12]  Abdl-Rahim, H.R., Zayed, M. and Ismail, G.M. (2022) Analytical Study of Fractional Epidemic Model via Natural Transform Homotopy Analysis Method. Symmetry, 14, Article 1695.
https://doi.org/10.3390/sym14081695
[13]  Ismail, G.M., Abdl-Rahim, H.R., Ahmad, H. and Chu, Y. (2020) Fractional Residual Power Series Method for the Analytical and Approximate Studies of Fractional Physical Phenomena. Open Physics, 18, 799-805.
https://doi.org/10.1515/phys-2020-0190
[14]  Ismail, G.M., Abdl-Rahim, H.R., Abdel-Aty, A., Kharabsheh, R., Alharbi, W. and Abdel-Aty, M. (2020) An Analytical Solution for Fractional Oscillator in a Resisting Medium. Chaos, Solitons & Fractals, 130, Article 109395.
https://doi.org/10.1016/j.chaos.2019.109395
[15]  Spiegel, M.R. (1965) Theory and Problems of Laplace Transforms. Schaums Outline Series. McGraw-Hill.
[16]  Debnath, L. (2005) Bhattforms Theory and Applications. Springer.
[17]  Belgacem, F.B.M., Karaballi, A.A. and Kalla, S.L. (2003) Analytical Investigations of the Sumudu Transformand Applications to Integral Production Equations. Mathematical Problems in Engineering, 2003, 103-118.
https://doi.org/10.1155/s1024123x03207018
[18]  Belgacem, F.B.M. and Karaballi, A.A. (2006) Sumudu Transform Fundamental Properties Investigations Andapplications. International Journal of Stochastic Analysis, 2006, Article 91083.
https://doi.org/10.1155/jamsa/2006/91083
[19]  Loonker, D. and Banerji, P.K. (2013) Solution of Fractional Ordinary Differential Equations by Natural Transform. International Journal of Mathematical Engineering and Science, 2, 2277-6982.
[20]  Podlubny, I. (1999) Fractional Differential Equations. In: Mathematics in Science and Engineering, Academic Press.
[21]  Caputo, M. and Fabrizio, M. (2015) A New Definition of Fractional Derivative without Singular Kernel Fractional Differential Equations. Progress in Fractional Differentiation and Applications, 2, 73-85.
[22]  Mittag-Leffler, G. (1903) Sur la Nouvelle Fonction Eα(x). Comptes Rendus de l’Academie des Sciences Paris, 137, 554-558.
[23]  Singh, G. and Singh, I. (2020) Laplace Transform Method for Solving Fourth Order Odes. International Conference of Futuristic Strategies of ICT for Digitalization and Sustainable Development, Jalandhar, 7-8 February 2020, 146-151.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133