Open Journal of mathematical Sciences (OMS)

The author considers a mathematical model of immunotherapy and anti-angiogenesis inhibitor therapy for cancer patients over a fixed time horizon. Disease dynamics are captured by a system of ODEs developed in [1], describing dynamics among host cells, cancer cells, endothelial cells, effector cells, and anti-angiogenesis. Existence, uniqueness, and characterization of optimal treatment profiles that minimize the tumor and drug usage, while maintaining healthy levels of effector and host cells are determined. A theoretical analysis is performed to characterize the optimal control. Numerical simulations are performed to illustrate optimal control profiles for a variety of different patients, each leading to different treatment protocols.

The objective of this paper is to investigate the existence and uniqueness theorem for stochastic partial differential equations with poisson jumps and delays. The existence of mild solutions of the problem is studied by using a different resolvent operator defined in [1] and fixed point theorem.

In this work, we study the small oscillations of a system formed by an elastic container with negligible density and a heavy barotropic gas (or a compressible fluid) filling the container. By means of an auxiliary problem, that requires a careful mathematical study, we deduce the problem to a problem for a gas only. From its variational formulation, we prove that is a classical vibration problem.

In this paper we define a new class of hyperholomorphic functions, which is known as \(F^{\alpha}_{G}(p,q,s)\) spaces. We characterize hyperholomorphic functions in \(F^{\alpha}_{G}(p,q,s)\) space in terms of the Hadamard gap in Quaternion analysis.

The effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by varying moving load resting on Vlasov foundation is investigated in this work. The problem is solved for concentrated loads with simply supported boundary conditions. An analytic solution based on the Galerkin’s method is used to reduce the fourth order partial differential equation into a system of coupled fourth order differential equation and a modification of the Struble’s technique and Laplace transforms are used to solve the resulting fourth order differential equation. Results obtained indicate that shear deformation and rotary inertia have significant effect on the dynamics of the anisotropic plate on the Vlasov foundation. Solutions are obtained for both the moving force and the moving mass problems. From the graphical results obtained, the amplitude of vibrations of the plate under moving mass is greater than that of the moving force and increasing the value of rotary inertia \({R_0}\) reduces the amplitude of vibration of the plate. increasing the mass ratio increases the amplitude of vibration of the plate.

Several neurodegenerative diseases such as Alzheimer’s Disease (AD), Huntington’s Disease (HD), Parkinson’s Disease (PD), and Amyotrophic Lateral Sclerosis (ALS) as well as ischemic strokes all show signs of excess oxidative stress due to increased production of reactive oxygen species (ROS). The author here posits here that ascorbic acid (AA), commonly known as Vitamin C, can help prevent such neurodegenerative disorders. The author proposes a mathematical model that captures the biochemical dynamics between AA, dehydroascorbic acid (DHA), and ROS in the brain and performs simulations under control and neurodegenerative disease situations. Then, a variety of treatments using AA and DHA were proposed and simulated to examine their efficacy.

A numerical study has been carried out in the analysis of two dimensional, incompressible and steady convective flow over a stretching surface in the presence of chemical reaction along with viscous dissipation. A mathematical model which resembles the physical flow problem has been developed. Similarity transformations are used to convert the fundamental partial differential equations into a system of nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations are then solved by using the shooting method along with Adams-Moultan method. The numerical solution obtained for the velocity, temperature and concentration profiles has been presented through graphs for different choice of the physical parameters.

The article investigates the behaviour of the multiplication table of the ring \(\mathbb{Z}_n\). To count the number of 1s appear on the main diagonal of the multiplication table of \(\mathbb{Z}_n\), conclusively an explicit formula is induced for any \(n \geq 2\).

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard-Fejér type inequality for generalized convex functions whose derivatives absolute values are generalized convex via local fractional integrals.

This work is concerned with a comparative study of performances of meshfree (radial basis functions) and mesh-based (finite difference) schemes in terms of their accuracy and computational efficiency while solving multi-dimensional initial-boundary value problems governed by a nonlinear time-dependent reaction-diffusion Brusselator system. For computing the approximate solution of the Brusselator system, we use linearly implicit Crank-Nicolson (LICN) scheme, Peaceman-Rachford alternating direction implicit (ADI) scheme and exponential time differencing locally one dimensional (ETD-LOD) scheme as mesh-based schemes and multiquadric radial basis function (MQRBF) as a meshfree scheme. A few numerical results are reported.