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Physical Sciences and Mathematics Commons™
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- Appell functions (1)
- Bernoulli sub-ODE method (1)
- Caputo derivative (1)
- Dixon’s theorem (1)
- Drinfeld-Sokolov-Wilson equation (1)
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- Extension formulas (1)
- Exton hypergeometric series (1)
- First integral method (1)
- Fractional calculus (1)
- Fractional differential equations (1)
- Gamma function (1)
- Generalized hypergeometric function (1)
- Homotopy (1)
- Jacobi polynomials (1)
- Lauricella functions (1)
- New exact solutions (1)
- Operational matrix (1)
- Perturbation Transform method (1)
- Perturbed nonlinear fractional Schr ¨odinger equation (1)
- Pochhammer symbol (1)
- Riccati equation (1)
- Tau method (1)
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Extension Formulas Of Lauricella’S Functions By Applications Of Dixon’S Summation Theorem, Ahmed A. Atash
Extension Formulas Of Lauricella’S Functions By Applications Of Dixon’S Summation Theorem, Ahmed A. Atash
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this research paper is to obtain two extension formulas for the first and second kind of Lauricella’s functions of three variables with the help of generalized Dixon’s summation theorem, which was obtained by Lavoie et al. In addition to this, two extension formulas for the second and third kind of Appell’s functions are obtained as a consequence of the above mentioned results . Furthermore, some transformation formulas involving Exton’s double hypergeometric series are obtained as an applications of our main results.
The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi
The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we have applied Jacobi polynomial to solve Riccati differential equation of fractional order. To do so, we have presented a general formula for the Jacobi operational matrix of fractional integral operator. Using the Tau method, the solution of this problem reduces to the solution of a system of algebraic equations. The numerical results for the examples presented in this paper demonstrate the efficiency of the present method.
New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods, Nasir Taghizadeh, Mona N. Foumani, Vahid S. Mohammadi
New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods, Nasir Taghizadeh, Mona N. Foumani, Vahid S. Mohammadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the fractional derivatives in the sense of the modified Riemann-Liouville derivative and the first integral method and the Bernoulli sub-ODE method are employed for constructing the exact complex solutions of the perturbed nonlinear fractional Schr ¨odinger equation and comparing the solutions.
Solution Of Fractional Drinfeld-Sokolov-Wilson Equation Using Homotopy Perturbation Transform Method, P. K. Singh, K. Vishal, T. Som
Solution Of Fractional Drinfeld-Sokolov-Wilson Equation Using Homotopy Perturbation Transform Method, P. K. Singh, K. Vishal, T. Som
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the approximate solutions of the non-linear Drinfeld-Sokolov-Wilson equation with fractional time derivative have been obtained. The fractional derivative is described in the Caputo sense. He’s polynomial is used to tackle the nonlinearity which arise in our considered problems. A time fractional nonlinear partial differential equation has been computed numerically. The numerical procedures illustrate the effectiveness and reliability of the method. Effects of fractional order time derivatives on the solutions for different particular cases are presented through graphs.