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A result on solvability for a class of nonlinear fractional integral equations in a Banach space

  • Sukanta Halder and Deepmala
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Nonlinear Analysis and Computational Techniques
This chapter is in the book Nonlinear Analysis and Computational Techniques

Abstract

This paper is concerned with the existence of solutions to a class of fractional functional integral equations in the Banach space C [ 0 , a ] , a > 0 . As our primary tool, we employ Petryshyn’s fixed point theorem associated with the measure of noncompactness. Our existence results contain several functional integral equations as a particular case that arises in nonlinear analysis. In addition, we provide some examples to illustrate the applicability of our results.

Abstract

This paper is concerned with the existence of solutions to a class of fractional functional integral equations in the Banach space C [ 0 , a ] , a > 0 . As our primary tool, we employ Petryshyn’s fixed point theorem associated with the measure of noncompactness. Our existence results contain several functional integral equations as a particular case that arises in nonlinear analysis. In addition, we provide some examples to illustrate the applicability of our results.

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/10.1515/9783111724638-005

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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