On the convergence of double Elzaki transform

Abstract

In this research, we have studied the convergence properties of Double Elzaki transformation and the results have been presented in the form of theorems on convergence, absolute convergence and uniform convergence of Double Elzaki transformation. The Double Elzaki transform of double Integral has also been discussed for integral evaluation. Finally, we have solved a Volterra integro-partial differential equation by using Double Elzaki transformation.

On two dimensional new integral transformation and its applications

“…We extend this definition of two dimensional generalized Elzaki -Tarig Transformation by using the definition [12] as;…”

“…are invertible function, thus from the definitions above it can be seen that it is the generalization of two dimensional [12] Elzaki -Tarig transformation.…”

Towards new general double integral transform and its applications to differential equations

“…Recently, double Laplace transform is used extensively to solve partial differential equations with unknown functions of two variables which obtained good results compared to numeric methods. 3,[17][18][19][20][21] Moreover, there exist in literature further extensions of double Laplace transform like double Sumudu transform, [22][23][24][25][26][27] double Shehu transform, 28 double Elzaki transform, 29 and double Ramadan group integral transform. 30 In 2020, the second and third authors have introduced new general integral transforms independently which are almost similar.…”

On the convergence of triple Elzaki transform

“…In the recent years, this transform has become more accurate and efficient. Elzaki transformation [3][4][5][6][7][8][9][10][11], introduced by Tarig Elzaki in 2011. Elzaki transform solving differential equations with variable coefficients, which are not solved, by Sumudu transform [12][13][14][15][16].…”