Bangmod International Journal of Mathematical and Computational Science

L-CATCH GUARANTEED PURSUIT TIME

Bashir Mai Umar — 2024-06-26

We consider a simple motion differential game of one pursuer and one evader. The dynamic equation of the pursuer and evader is describe by first order and second order differential equation respectively. Control functions of the players are subject to integral constraints. We show that pursuit is completed in L-catch sense, that is for some distance L , the difference in positions of the pursuit and evader x(t) and y(t) respectively is smaller than L that is ||y(t) - x(t)||< L at some time t . We construct a formula for guaranteed pursuit time and prove that pursuit is possible at that time.

RELAXED DOUBLE INERTIA AND VISCOSITY ALGORITHMS FOR THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS

Solomon Gebregiorgis — 2024-06-29

In this paper, we investigate a multiple-sets split feasibility problem with multiple output sets in infinite-dimensional Hilbert spaces. To address this problem, we propose relaxed inertial self-adaptive algorithms that do not use the least squares method and prove strong convergence results for the sequences generated by these algorithms. Finally, we validate the performances of the proposed algorithms by using numerical examples.

EXISTENCE OF SOLUTION OF MULTI-TERM FRACTIONAL ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATION

Dahiru Umar — 2024-07-12

This paper considered a multi-term fractional order Fredholm integro-differential equation. The multi-term fractional order Fredholm integro-differential equation was transformed into its corresponding integral equation form with the help of Riemann-Liouville fractional integral by which, Schauder’s fixed point theorem is utilised in the study and establishing the existence of solution for the multi-term fractional order Fredholm integro-differential equation. Moreover, some examples were considered to prove the claim of the established existence of solution theorem.

A NEW CONVERGENCE ANALYSIS FOR MINIMUM NORM SOLUTION OF SPLIT SYSTEM OF NONSMOOTH MINIMIZATION PROBLEMS

Anteneh Getachew Gebrie — 2024-08-06

This work presents a novel self-adaptive steepest-descent type algorithm for solving the split system of minimization problem (SSMP) related to convex nonsmooth functions. The algorithm includes a self-adaptive step size mechanism, which uses a step size that does not need prior information about the operator norm. Under certain weakened assumptions of parameters, a strong convergence theorem is established and proved for the algorithm. Specifically, the sequence generated by this new algorithm strongly converges towards the minimum norm element of the SSPM. To assess the implementation of our algorithm, a numerical example is provided. According to the numerical results, our algorithm showcases effectiveness and simplicity in its implementation. Furthermore, the primary numerical experiment results indicate that our proposed algorithm surpasses some existing results in the literature in terms of CPU time and iteration count. Our result represents an extension and enhancement of recent findings in this area.

RESULTS ON IMPULSIVE ψ-CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS

Kuppusamy Venkatachalam — 2024-10-02

In this research article, we investigate the existence and uniqueness of solutions for a type of boundary value problems involving fractional integro-differential equations with the ψ-Caputo fractional derivative. Our method utilizes several classical fixed point theorems, such as the Banach contraction principle and Krasnoselskii's fixed point theorem. We establish our main results through theoretical analysis and present a specific case study to illustrate the practical significance of our findings.