Python Approach For Solving Fractional Order Modified KdV Burger's Equation By Adomian Decomposition Method

Authors

  • Chittaranjan Pawar Department of Mathematics, C.H.M.E. Society's Bhonsala Military College, Nashik-422005, (M.S.), India. https://orcid.org/0009-0009-5216-078X
  • Kalyanrao Takale
  • Shrikisan Gaikwad

Keywords:

Fractional order Differential Equation, FractionalCaputo Derivative, ADM, KDV Burger equation, Python

Abstract

The present work is devoted to solve fractional order modified KdV Burger's equation. We consider a time fractional order modified KDV Burger's equation in the Caputo sense. Adomian decomposition method is employ to find the approximate solution of this equation. We developed Python programme for Adomian Decomposition Method to find numerical solutions. We obtained the approximate solutions of time fractional order modified KDV Burger's equation by considering higher nonlinearity. The obtained results are compared with exact solution. The Adomian Decomposition Method provides an approach for approximating the solution of highly non-linear equations of fractional order.

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References

Alderremy A.A., Aly S., Fayyaz R., Khan A., Shah R., Wyal N. The Analysis of Fractional-

Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform.

Complexity [Internet]. 2022;2022. doi:10.1155/2022/4935809

Alqahtani Z., Hagag A.E. A new semi-analytical solution of compound KdV-Burgers equation

of fractional order. Revista Internacional de M´etodos Num´ericos para C´alculo y Dise˜no

en Ingenier´ıa [Internet]. 2023;39. doi:10.23967/j.rimni.2023.10.003

Atta, A. G. and Youssri, Y. H. (2023). Shifted Second-Kind Chebyshev Spectral Collocation-

Based Technique for Time-Fractional KdV-Burgers’ Equation. Iranian Journal of Mathematical

Chemistry, 14(4). doi:10.22052/IJMC.2023.252824.1710

Balachandran K. Fractional Differential Equations. In: Industrial and Applied Mathematics

[Internet]. Cham: Springer; 2023. p. 51–85.

Sonawane J., Sonatakke B., Takale K. Numerical Solution of Subdiffusion Bioheat equation

with Single Phase lag. Indian Journal of Science and Technology [Internet]. 2024;17:955–

Deng, S. and Deng, Z. (2023). Approximate analytical solutions for a class of generalized

perturbed KdV-Burgers equation. Thermal Science, 27(3). doi:10.2298/TSCI2303881D

Ganie A.H., Mofarreh F., Khan A. On new computations of the time-fractional nonlinear

KdV–Burgers equation with exponential memory. Physica Scripta. 2024;99(045217).

doi:10.1088/1402-4896/ad2e60

Gaur, M. (2023). Symmetry analysis of conformable fractional coupled KdV–Burgers equation.

Palestine Journal of Mathematics, 12(1).

Rida S.Z., Hussien H.S. Efficient Computational Approach for Generalized Fractional KdV–

Burgers Equation. International Journal of Applied and Computational Mathematics [Internet].

;6. doi:10.1007/s40819-020-00915-1

Hashemi, M. S., Inc, M., and Baleanu, D. (2019). On fractional KdV-Burgers and potential

KdV equations: Existence and uniqueness results. Thermal Science, 23, S2107–S2117.

Heydari M.H., Avazzadeh Z., Cattani C. Numerical solution of variable-order

space-time fractional KdV–Burgers–Kuramoto equation. Engineering with Computers.

;38:859–869.

Khan A., Akram T., Khan A., Ahmad S., Nonlaopon K. Investigation of time fractional

nonlinear KdV–Burgers equation under fractional operators with nonsingular kernels. AIMS

Mathematics. 2023;8:1251–1268.

Khuri S.A. Traveling wave solutions for nonlinear differential equations: A unified ans¨atze

approach. Chaos, Solitons and Fractals. 2007;32(1).

Kulkarni S., Takale K., Shaikh A. Application of Adomian decomposition method to solve

the fractional mathematical model of coronavirus. Journal of Mathematics and Computational

Science. 2020;10:1327–1339.

Li W., Pang Y. Application of Adomian decomposition method to nonlinear systems. Advances

in Differential Equations. 2020;2020.

Nieto J.J., Rodr´ıguez-L´opez R. Fractional Differential Equations. MDPI; 2020.

Pawar, C., Takale, K., and Gaikwad, S. (2024). Comparative Study of Solutions of Fractional

Order Mixed KdV Burger’s Equation. Indian Journal of Science and Technology, 17(25),

–2598.

Takale K., Kharde U., Takale G. Fractional Order Mathematical Model to Investigate Topical

Drug Diffusion in Human Skin. Indian Journal of Science and Technology. 2023;16:4657–

Zada L., Aziz I. The numerical solution of fractional Korteweg-de Vries and Burgers’

equations via Haar wavelet. Mathematical Methods in the Applied Sciences. 2021;44:10564–

Zeng, H., Wang, Y., Xiao, M., and Wang, Y. (2023). Fractional solitons: New phenomena

and exact solutions. Frontiers in Physics, 11.

Wei L., Wei X., Tang B. Numerical analysis of variable-order fractional

KdV–Burgers–Kuramoto equation. Electronic Research Archive. 2022;30:1263–1281.

Published

June 30, 2026

Issue

Section

Research Article

How to Cite

Pawar, C., Kalyanrao Takale, & Shrikisan Gaikwad. (2026). Python Approach For Solving Fractional Order Modified KdV Burger’s Equation By Adomian Decomposition Method. Communications in Mathematics and Applications, 17(2). https://doi.org/10.26713/cma.v17i2.3457