Displaying similar documents to “q-fractional differentiation and basic hypergeometric transformations”

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Yadav, R., Purohit, S., Kalla, S. (2008)

Fractional Calculus and Applied Analysis

Similarity:

Mathematics Subject Classification: 33D60, 33D90, 26A33 Fractional q-integral operators of generalized Weyl type, involving generalized basic hypergeometric functions and a basic analogue of Fox’s H-function have been investigated. A number of integrals involving various q-functions have been evaluated as applications of the main results.

Exact solution of the time fractional variant Boussinesq-Burgers equations

Bibekananda Bira, Hemanta Mandal, Dia Zeidan (2021)

Applications of Mathematics

Similarity:

In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs)...

Fractional-order Bessel functions with various applications

Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi (2019)

Applications of Mathematics

Similarity:

We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error...

Extended Riemann-Liouville type fractional derivative operator with applications

P. Agarwal, Juan J. Nieto, M.-J. Luo (2017)

Open Mathematics

Similarity:

The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented. ...