-
Research Article
Quadruple Laplace-Sumudu-Aboodh-Elzaki Transform and Its Applications
Issue:
Volume 13, Issue 5, October 2025
Pages:
308-319
Received:
28 June 2025
Accepted:
9 July 2025
Published:
5 September 2025
Abstract: This research introduces an approach that combines four different transforms such as Laplace transform, Sumudu transform, Aboodh transform and Elzaki transform to produce a quadruple transform. We state and apply the quadruple transform for several functions of four variables and went further to proof some fundamental properties and theorems. The existence analysis of the method and partial derivatives theorems were proven. Moreover, we examined how efficient and applicable the transform is by applying it to some integral equations and partial differential equations.
Abstract: This research introduces an approach that combines four different transforms such as Laplace transform, Sumudu transform, Aboodh transform and Elzaki transform to produce a quadruple transform. We state and apply the quadruple transform for several functions of four variables and went further to proof some fundamental properties and theorems. The e...
Show More
-
Research Article
On the Existence and Uniqueness of Solution of Non-linear Fractional Differential Equations with Integral Boundary Condition
Issue:
Volume 13, Issue 5, October 2025
Pages:
320-338
Received:
5 July 2025
Accepted:
11 August 2025
Published:
12 September 2025
Abstract: In this paper, we investigate the Existence and Uniqueness of solutions of non-linear fractional boundary value differential equations with integral boundary condition using the method of Upper and Lower solutions. We employed the contraction mapping principle and Schauder fixed point theorems. We find out from the analysis that the solution of the boundary value fractional differential equation exists and is unique. An Adomian decomposition method is also used to construct the algorithm for the numerical solution of the nonlinear fractional differential equation. Further, for the implementation of the Adomian decomposition method, several numerical examples are constructed to demonstrate the applicability, accuracy, efficiency, and effectiveness of the method. The results show that the method is accurate and efficient in approximating the exact solution.
Abstract: In this paper, we investigate the Existence and Uniqueness of solutions of non-linear fractional boundary value differential equations with integral boundary condition using the method of Upper and Lower solutions. We employed the contraction mapping principle and Schauder fixed point theorems. We find out from the analysis that the solution of the...
Show More
-
Research Article
Efficient Algorithms for Critical Node Detection on Path Graphs with Binary Connection Metrics
Syed Md Omar Faruk*
,
Kamrun Nahar Jabin
Issue:
Volume 13, Issue 5, October 2025
Pages:
339-343
Received:
9 August 2025
Accepted:
18 August 2025
Published:
25 September 2025
Abstract: This paper investigates the Critical Node Detection Problem (CNDP) on path graphs where connection costs between node pairs are binary (0 or 1). Two variants of the problem are explored based on whether node weights are uniform or arbitrary. For both cases, the objective is to identify a subset of nodes whose removal minimizes the number of important connections surviving. Efficient dynamic programming algorithms are proposed to solve these problems optimally. When node weights are uniform, the approach runs in O(n3K) time, where n is the number of nodes and K is the maximum number of deletions allowed. For arbitrary node weights with a total removal budget W, the solution is derived in O(n5) time.
Abstract: This paper investigates the Critical Node Detection Problem (CNDP) on path graphs where connection costs between node pairs are binary (0 or 1). Two variants of the problem are explored based on whether node weights are uniform or arbitrary. For both cases, the objective is to identify a subset of nodes whose removal minimizes the number of importa...
Show More
