# fractional partial differential equationsRecently Published Documents

483
(FIVE YEARS 188)

## H-INDEX

38
(FIVE YEARS 8)

2022 ◽
Vol 124 ◽
pp. 107644
Author(s):
Xuehua Yang ◽
Haixiang Zhang

Author(s):
Kumbinarasaiah Srinivasa

Abstract This paper generates a novel approach called the clique polynomial method (CPM) using the clique polynomials raised in graph theory and used for solving the fractional order PDE. The fractional derivative is defined in terms of the Caputo fractional sense and the fractional partial differential equations (FPDE) are converted into nonlinear algebraic equations and collocated with suitable grid points in the current approach. The convergence analysis for the proposed scheme is constructed and the technique proved to be uniformly convegant. We applied the method for solving four problems to justify the proposed technique. Tables and graphs reveal that this new approach yield better results. Some theorems are discussed with proof.

2022 ◽
Vol 2022 ◽
pp. 1-20
Author(s):
Hossein Aminikhah

This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method.

2022 ◽
Vol 41 (1) ◽
Author(s):
Prashant Pandey ◽
Jagdev Singh

2021 ◽
Vol 2021 ◽
pp. 1-8
Author(s):
Jafar Biazar ◽
Saghi Safaei

In this article, a comparative study between optimal homotopy asymptotic method and multistage optimal homotopy asymptotic method is presented. These methods will be applied to obtain an approximate solution to the seventh-order Sawada-Kotera Ito equation. The results of optimal homotopy asymptotic method are compared with those of multistage optimal homotopy asymptotic method as well as with the exact solutions. The multistage optimal homotopy asymptotic method relies on optimal homotopy asymptotic method to obtain an analytic approximate solution. It actually applies optimal homotopy asymptotic method in each subinterval, and we show that it achieves better results than optimal homotopy asymptotic method over a large interval; this is one of the advantages of this method that can be used for long intervals and leads to more accurate results. As far as the authors are aware that multistage optimal homotopy asymptotic method has not been yet used to solve fractional partial differential equations of high order, we have shown that this method can be used to solve these problems. The convergence of the method is also addressed. The fractional derivatives are described in the Caputo sense.

2021 ◽
Vol 10 (4) ◽
pp. 607-615
Author(s):
R. Ramesh ◽
P. Prakash ◽
S. Harikrishnan

2021 ◽
Vol 61 (12) ◽
pp. 2024-2033
Author(s):
M. Shareef Ajeel ◽
M. Gachpazan ◽
Ali R. Soheili

Author(s):
Mo Faheem ◽
Akmal Raza

2021 ◽
Vol 5 (4) ◽
pp. 208
Author(s):
Md. Habibur Rahman

A multidimensional, modified, fractional-order B-polys technique was implemented for finding solutions of linear fractional-order partial differential equations. To calculate the results of the linear Fractional Partial Differential Equations (FPDE), the sum of the product of fractional B-polys and the coefficients was employed. Moreover, minimization of error in the coefficients was found by employing the Galerkin method. Before the Galerkin method was applied, the linear FPDE was transformed into an operational matrix equation that was inverted to provide the values of the unknown coefficients in the approximate solution. A valid multidimensional solution was determined when an appropriate number of basis sets and fractional-order of B-polys were chosen. In addition, initial conditions were applied to the operational matrix to seek proper solutions in multidimensions. The technique was applied to four examples of linear FPDEs and the agreements between exact and approximate solutions were found to be excellent. The current technique can be expanded to find multidimensional fractional partial differential equations in other areas, such as physics and engineering fields.

2021 ◽
Author(s):