About the Solution Stability of Volterra Integral Equation With Random Kernel

Alexandria Engineering Journal

Qazza

et al. 2023

Section: Introductionmentioning

confidence: 99%

ARA-residual power series method for solving partial fractional differential equations

Alexandria Engineering Journal

Qazza

et al. 2023

“…Numerous phenomena in various elds of science can be fruitfully formulated by the use of fractional derivatives. is is because the sensible modeling for a physical phenomenon depends on instantaneous time as well as on prior time history; hence, we may use fractional calculus to deal with these problems [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Qazza

Mathematical Problems in Engineering

2022

In this research, systems of linear and nonlinear differential equations of fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on the combination of the residual power series scheme with the ARA transform to establish analytical approximate solutions in a fast convergent series representation using the concept of the limit. The proposed method needs less time and effort compared with the residual power series technique. To prove the simplicity, applicability, and reliability of the presented method, three numerical examples are proposed and simulated. The obtained results show that the ARA-RPS technique is applicable, simple, and effective to get solutions to linear and nonlinear engineering and physical problems.

show abstract

“…some of these integrals can't be solved up to now, some of them are solved numerically, and there still some integrations that cannot be determined exactly or need much effort to be solved. The importance of computing improper integrals has come from the wide usage in applied math, physics, engineering and etc., [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

New Theorems in Solving Families of Improper Integrals

Abu-Ghuwaleh

2022

Axioms