## THERMAL SCIENCE

International Scientific Journal

### ANALYTIC ALGORITHM FOR LOCAL FRACTIONAL CAUDREY-DODD-GIBBON-KAEADA EQUATION BASED ON THE NEW ITERATIVE METHOD

**ABSTRACT**

In this paper, the initial value problem is discussed for the local fractional Caudrey-Dodd-Gibbon-Kaeada equation. The fractional complex transform and the new iterative method are used to solve the problem, and the approximate analytical solutions are obtained.

**KEYWORDS**

PAPER SUBMITTED: 2020-11-05

PAPER REVISED: 2021-10-01

PAPER ACCEPTED: 2021-10-01

PUBLISHED ONLINE: 2022-07-16

**THERMAL SCIENCE** YEAR

**2022**, VOLUME

**26**, ISSUE

**Issue 3**, PAGES [2771 - 2778]

- Yang, X.-J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 151 (2017), 1-4, pp. 63-75
- Yang, X.-J., et al., New Rheological Models Within Local Fractional Derivative, Romanian Reports in Physics, 69 (2017), 3, 113
- Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Itera-tion Method, Thermal Science, 2 (2013), 17, pp. 625-628
- Yang, A. M., et al., Picard Successive Approximation Method for Solving Differential Equations Aris-ing in Fractal Heat Transfer with Local Fractional Derivative, Abstract and Applied Analysis, 2 (2014), 2014, pp. 1-5
- Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 21501826
- Habib, S., et al., Study of Non-linear Hirota-Satsuma Coupled KdV and Coupled mKdV System with Time Fractional Derivative, Fractals, 29 (2021), 5, 2150108
- Shi, Y. Q., et al., The Multi-Wave Method for Non-linear Evolution Equations, Mathematical and Com-putational Applications, 15 (2011), 5, pp. 776-783
- Fan, E.G., Traveling Wave Solutions for Non-linear Equations Using Symbolic Computation, Comput-ers and Mathematics with Applications, 43 (2002), 6-7, pp. 671-680
- Wazwaz, A. M., Analytic Study of the Fifth Order Integrable Non-linear Evolution Equations by Using the Tanh Method, Applied Mathematics and Computation, 174 (2006), 1, pp. 289-299
- Wazwaz, A. M., Multiple-Soliton Solutions for the Fifth Order Caudrey-Dodd-Gibbon Equation, Ap-plied Mathematics and Computation, 197 (2008), 2, pp. 719-724
- Yang, Y. J., The Extended Variational Iteration Method for Local Fractional Differential Equation, Thermal Science, 25 (2021), 2, pp. 1509-1516
- Yang, Y. J., The Local Fractional Variational Iteration Method: A Promising Technology for Fractional Calculus, Thermal Science, 24 (2020), 4, pp. 2605-2614
- Nadeem, M., He, J. H., He-Laplace Variational Iteration Method for Solving the Non-linear Equations Arising in Chemical Kinetics and Population Dynamics, Journal of Mathematical Chemistry, 59 (2021), 5, pp. 1234-1245
- He, J.‐H., et al., Homotopy Perturbation Method for the Fractal Toda Oscillator, Fractal Fract., 5 (2021), 93
- He, J. H., El-Dib, Y. O., Periodic Property of the Time-Fractional Kundu-Mukherjee-Naskar Equation, Results in Physics, 19 (2020), Dec., 103345
- Jafari, H., Jassim, H. K., Local Fractional Series Expansion Method for Solving Laplace and Schroding-er Equations on Cantor Sets within Local Fractional Operators, International Journal of Mathematics and Computer Research, 11 (2014), 2, pp. 736-744
- Wang, S. Q., et al., Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014, Article ID 176395
- Daftardar-Gejji, V., Jafari, H., An Iterative Method for Solving Non-linear Functional Equations, Jour-nal of Mathematical Analysis and Applications, 316 (2006), 2, pp. 753-763
- Bhalekar, S., Daftardar-Gejji, V., New Iterative Method: Application to Partial Differential Equations, Applied Mathematics and Computation, 203 (2008), 2, pp. 778-783
- Daftardar-Gejji, V., and Bhalekar, S. Solving Fractional Boundary Value Problems with Dirichlet Boundary Conditions Using a New Iterative Method, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1801-1809
- He, J. H., Li, Z. B., Converting Fractional Differential Equations Into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
- Li, Z. B., et al., Exact Solutions of Time Fractional Heat Conduction Equation by the Fractional Com-plex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
- Ain, Q. T., et al., The Fractional Complex Transform: A Novel Approach to the Time-Fractional Scho-dinger Equation, Fractals, 28 (2020), 7, 2050141
- Anjum, N., Ain, Q. T., Application of He's Fractional Derivative and Fractional Complex Transform for Time Fractional Camassa-Holm Equation, Thermal Science, 24 (2020), 5, pp. 3023-3030
- He, J. H., et al., A Fractal Modification of Chen-Lee-Liu Equation and Its Fractal Variational Principle, International Journal of Modern Physics B, 35 (2021), 21, 2150214
- He, J. H., Seeing with a Single Scale is Always Unbelieving: From Magic to Two-Scale Fractal, Ther-mal Science, 25 (2021), 2, pp. 1217-1219
- He, J. H., et al., Solitary Waves Travelling Along an Unsmooth Boundary, Results in Physics, 24 (2021), May, 104104
- Nadeem, M., He, J. H., The Homotopy Perturbation Method for Fractional Differential Equations: Part 2, Two-Scale Transform, International Journal of Numerical Methods for Heat & Fluid Flow, 32 (2021), 2, pp. 559-567
- He, J. H., et al., Evans Model for Dynamic Economics Revised, AIMS Mathematics, 6 (2021), 9, pp. 9194-9206
- He, J. H., et al., Variational Approach to Fractal Solitary Waves, Fractals, 29 (2021), 7, 2150199
- Feng, G. Q., He's Frequency Formula to Fractal Undamped Duffing Equation, Journal of Low Frequen-cy Noise Vibration and Active Control, 40 (2021), 4, pp. 1671-1676
- Tian, Y., Liu, J., Direct Algebraic Method for Solving Fractional Fokas Equation, Thermal Science, 25 (2021), 3, pp. 2235-2244
- Han, C., et al., Numerical Solutions of Space Fractional Variable-Coefficient KdV-Modified KdV Equa-tion by Fourier Spectral Method，Fractals, 29 (2021), 8, pp. 1-19
- Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 21501826