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Analysis of atmospheric C O 2 gas dynamics via fractional generalized homotopy analysis method

  • Kanthasamy Jayaram Prakash , Sathiyamoorthy Ravisankar Saratha and Azhagarswamy Geethakarthi
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Nonlinear Analysis and Computational Techniques
This chapter is in the book Nonlinear Analysis and Computational Techniques

Abstract

This study presents a fractional-order mathematical model of three nonlinear differential equations capturing the interaction between human population dynamics, forest biomass, and atmospheric C O 2 gas concentration. Additionally, the stability of the proposed model is analyzed. A new approach is presented, combining the Laplace-type integral transform with the homotopy analysis method, showcasing its effectiveness in handling systems with fractional orders. The systematic approach and high efficacy of the proposed method in understanding the behavior of fractional-order differential equations in practical scenarios are confirmed by findings of this research. The increase in the atmospheric C O 2 levels with an increase in human population and a decrease in forest biomass was observed from various inputs of fractional orders and confirmed by the convergence of the series solutions using the homotopy parameter.

Abstract

This study presents a fractional-order mathematical model of three nonlinear differential equations capturing the interaction between human population dynamics, forest biomass, and atmospheric C O 2 gas concentration. Additionally, the stability of the proposed model is analyzed. A new approach is presented, combining the Laplace-type integral transform with the homotopy analysis method, showcasing its effectiveness in handling systems with fractional orders. The systematic approach and high efficacy of the proposed method in understanding the behavior of fractional-order differential equations in practical scenarios are confirmed by findings of this research. The increase in the atmospheric C O 2 levels with an increase in human population and a decrease in forest biomass was observed from various inputs of fractional orders and confirmed by the convergence of the series solutions using the homotopy parameter.

Chapters in this book

  1. Frontmatter I
  2. Contents V
  3. Fixed points and their geometric properties for interpolative contravariant mappings 1
  4. Coupled fixed point theorems for F-contraction mappings in S-metric spaces 15
  5. Fixed point theorems in convex C ∗ -algebra-valued fuzzy soft metric spaces with application in medical imaging 39
  6. Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series 55
  7. A result on solvability for a class of nonlinear fractional integral equations in a Banach space 73
  8. Solvability of Hadamard fractional integral equations via fixed point theorem 87
  9. Improved pseudospectral approximation for nonlinear parabolic equation 99
  10. Analysis of atmospheric C O 2 gas dynamics via fractional generalized homotopy analysis method 109
  11. A numerical scheme based on Galerkin method for solving singularly perturbed differential equation with mixed shifts 127
  12. Influence of urbanization and climate change on the human population through a mathematical modeling 143
  13. Effect of preservation on an EPQ model with selling and credit period-dependent demand under carbon tax policy 157
  14. Optimal homotopy solution of the sine-Gordon equation 175
  15. Significance of chemical interactions and thermal transpiration on transient MHD-free convective heat and mass transport over an infinite plate via porous media 191
https://doi.org/10.1515/9783111724638-008

Chapters in this book

  1. Frontmatter I
  2. Contents V
  3. Fixed points and their geometric properties for interpolative contravariant mappings 1
  4. Coupled fixed point theorems for F-contraction mappings in S-metric spaces 15
  5. Fixed point theorems in convex C ∗ -algebra-valued fuzzy soft metric spaces with application in medical imaging 39
  6. Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series 55
  7. A result on solvability for a class of nonlinear fractional integral equations in a Banach space 73
  8. Solvability of Hadamard fractional integral equations via fixed point theorem 87
  9. Improved pseudospectral approximation for nonlinear parabolic equation 99
  10. Analysis of atmospheric C O 2 gas dynamics via fractional generalized homotopy analysis method 109
  11. A numerical scheme based on Galerkin method for solving singularly perturbed differential equation with mixed shifts 127
  12. Influence of urbanization and climate change on the human population through a mathematical modeling 143
  13. Effect of preservation on an EPQ model with selling and credit period-dependent demand under carbon tax policy 157
  14. Optimal homotopy solution of the sine-Gordon equation 175
  15. Significance of chemical interactions and thermal transpiration on transient MHD-free convective heat and mass transport over an infinite plate via porous media 191
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