Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series
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Biniyam Shimelis
Abstract
In light of many applications in the natural and social sciences, the fractional q-calculus has received a lot of interest from researchers in a wide range of fields throughout the last forty years or so. Many operators in fractional q-calculus, notably those involving distinct q-special functions, have been extensively researched and are widely utilized in practice. In this paper, we establish particular image formulas for Saigo fractional q-derivative operators. These image formulas involve the multiplication of a general class of q-polynomials and generalized q-hypergeometric series and are stated in terms of generalized q-hypergeometric series. In addition, we investigate fascinating particular situations of our main findings and draw pertinent linkages between our results and earlier studies.
Abstract
In light of many applications in the natural and social sciences, the fractional q-calculus has received a lot of interest from researchers in a wide range of fields throughout the last forty years or so. Many operators in fractional q-calculus, notably those involving distinct q-special functions, have been extensively researched and are widely utilized in practice. In this paper, we establish particular image formulas for Saigo fractional q-derivative operators. These image formulas involve the multiplication of a general class of q-polynomials and generalized q-hypergeometric series and are stated in terms of generalized q-hypergeometric series. In addition, we investigate fascinating particular situations of our main findings and draw pertinent linkages between our results and earlier studies.
Chapters in this book
- Frontmatter I
- Contents V
- Fixed points and their geometric properties for interpolative contravariant mappings 1
- Coupled fixed point theorems for F-contraction mappings in S-metric spaces 15
-
Fixed point theorems in convex
- Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series 55
- A result on solvability for a class of nonlinear fractional integral equations in a Banach space 73
- Solvability of Hadamard fractional integral equations via fixed point theorem 87
- Improved pseudospectral approximation for nonlinear parabolic equation 99
-
Analysis of atmospheric
- A numerical scheme based on Galerkin method for solving singularly perturbed differential equation with mixed shifts 127
- Influence of urbanization and climate change on the human population through a mathematical modeling 143
- Effect of preservation on an EPQ model with selling and credit period-dependent demand under carbon tax policy 157
- Optimal homotopy solution of the sine-Gordon equation 175
- Significance of chemical interactions and thermal transpiration on transient MHD-free convective heat and mass transport over an infinite plate via porous media 191
Chapters in this book
- Frontmatter I
- Contents V
- Fixed points and their geometric properties for interpolative contravariant mappings 1
- Coupled fixed point theorems for F-contraction mappings in S-metric spaces 15
-
Fixed point theorems in convex
- Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series 55
- A result on solvability for a class of nonlinear fractional integral equations in a Banach space 73
- Solvability of Hadamard fractional integral equations via fixed point theorem 87
- Improved pseudospectral approximation for nonlinear parabolic equation 99
-
Analysis of atmospheric
- A numerical scheme based on Galerkin method for solving singularly perturbed differential equation with mixed shifts 127
- Influence of urbanization and climate change on the human population through a mathematical modeling 143
- Effect of preservation on an EPQ model with selling and credit period-dependent demand under carbon tax policy 157
- Optimal homotopy solution of the sine-Gordon equation 175
- Significance of chemical interactions and thermal transpiration on transient MHD-free convective heat and mass transport over an infinite plate via porous media 191
