-
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
-
Research Article
Explicit Construction of a Parametric Family of Elliptic Curves of Rank 4 via a Quadratic Extension
Issue:
Volume 13, Issue 5, October 2025
Pages:
344-347
Received:
14 August 2025
Accepted:
17 September 2025
Published:
22 October 2025
DOI:
10.11648/j.ajam.20251305.14
Downloads:
Views:
Abstract: We present an explicit one-parameter family of elliptic curves defined over ℚ(t) possessing at least four independent rational points, where the fourth point is defined over a quadratic extension. By specializing at t0= −842/35, we compute the Néron-Tate height pairing matrix of these points numerically using SageMath, establishing their linear independence and hence the curve’s rank of at least 4. This construction builds upon interpolation techniques and explicit extension field definitions, contributing a concrete example in the study of high rank elliptic curve families.
Abstract: We present an explicit one-parameter family of elliptic curves defined over ℚ(t) possessing at least four independent rational points, where the fourth point is defined over a quadratic extension. By specializing at t0= −842/35, we compute the Néron-Tate height pairing matrix of these points numerically using SageMath, establishing their line...
Show More
-
Research Article
Heat Source and Chemical Reaction Effects on the Unsteady Radiative Free Convection Flow of Conducting Fluid from an Impulsively Started Infinite Vertical Plate in the Presence of Magnetic Field
Issue:
Volume 13, Issue 5, October 2025
Pages:
348-359
Received:
11 August 2025
Accepted:
8 September 2025
Published:
22 October 2025
DOI:
10.11648/j.ajam.20251305.15
Downloads:
Views:
Abstract: An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneous chemical reaction of first order. By systematically transforming the governing set of partial differential equations into non dimensional form using selected similarity variables. An exact analytical solution is obtained from the dimensionless governing equations by using Laplace transform technique and inverse Laplace transform technique. The velocity, temperature and concentration profiles are presented for different existing flow parameters with the help of graphical representation. The velocity of the conducting fluid decreases with increasing magnetic parameter, heat absorption parameter, chemical reaction parameter and the velocity increases with increasing buoyancy parameter and time. The temperature of the fluid decreases with increasing the Prandtl number, heat absorption parameter and increases with increasing time. Similarly, the concentration of the fluid decreases with increasing the Schmidt number, chemical reaction parameter and increases with increasing time. The velocity, temperature and concentration profiles are studied for different existing parameters have been compared with earlier published works and the present results are found good agreement with the published results. The skin friction co-efficient, Nussult number and Sherwood number have also been calculated for all the existing parameters in this paper. Skin-friction decreases with increasing the magnetic parameter but skin friction increases with the increasing chemical reaction parameter, Prandtl number, Schmidt number, heat absorption parameter and time. No magnetic effect is observed on Nusselt and Sherwood number but with the increase of Prandtl number and Schmidt number, Nusselt number and Sherwood number are seen to increase respectively but both decrease with increasing time.
Abstract: An investigation is made on the unsteady electrically conducting Newtonian fluid flow past a suddenly started vertical infinite flat plate under the influence of heat and mass transfer in the presence of magnetic field. The radiation and heat absorption effects are studied in this investigation. Mass diffusion are taken in to account the homogeneou...
Show More
-
Research Article
Unified Approaches to Congruent Numbers via Geometry, Elliptic Curves and Arithmetic Progression of Squares
Issue:
Volume 13, Issue 5, October 2025
Pages:
360-364
Received:
22 August 2025
Accepted:
23 September 2025
Published:
22 October 2025
DOI:
10.11648/j.ajam.20251305.16
Downloads:
Views:
Abstract: We explore congruent numbers through a unified approach combining geometric constructions, elliptic curve theory, and arithmetic progressions of squares. Leveraging recent advances in modular forms and computational techniques, we construct infinite explicit families of congruent numbers parameterized by Pell-type equations and related Diophantine conditions. We complement this with a detailed statistical analysis of the residue classes, rank distributions, and root numbers associated with these families, providing empirical insights that deepen understanding of intricate conjectures in the arithmetic of elliptic curves.
Abstract: We explore congruent numbers through a unified approach combining geometric constructions, elliptic curve theory, and arithmetic progressions of squares. Leveraging recent advances in modular forms and computational techniques, we construct infinite explicit families of congruent numbers parameterized by Pell-type equations and related Diophantine ...
Show More
