Open Access Method Article

Construction of Functions for Fractional Derivatives using Matlab

Olagunju Adeyemi Sunday, Joseph Folake Lois

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2021/v36i630368

MATLAB is a high level programming tool for technical computing, its application cuts across different sphere of science, engineering, finance, communication, music etc. With the current increase in the use of non-integer order derivatives, there is a need to have tools that handle them for effective applications. In this paper, we present a brief comparative review of 2 expressions of fractional derivative. MATLAB functions for approximating Riemann-Liouville and Caputo fractional derivatives are presented alongside. Numerical simulations with test examples are implemented and results compared. To effectively handle non-polynomial function, Taylor series expansion is employed to convert the function into a form that can be easily handled.

Open Access Original Research Article

Numerical Approximations of ODEs Initial Value Problem; A Case Study of Gluconic Acid Fermentation by Pseudomonas ovalis

N. A. Ihoeghian, B. O. John

Journal of Advances in Mathematics and Computer Science, Page 11-23
DOI: 10.9734/jamcs/2021/v36i630369

Across different sections of life, physical and chemical sciences, differential equations which could be ordinary differential equations (ODEs) or partial differential equations (PDEs) are used to model the various systems as observed. Some types of ODEs, and a few PDEs are solvable by analytical methods with much difficulties. However, the great majority of ODEs, especially the non-linear ones and those that involve large sets of simultaneous differential equations, do not have analytical solutions but require the application of numerical techniques.  This work focused on exemplifying numerical approximations (Adams-Bashforth-Moulton, Bogacki-Shampine, Euler) of ODEs Initial value Problem in its simplest approach using a case study of gluconic acid frementation by Psuedonomas Ovalis. The performance of the methods was checked by comparing their accuracy.  The accuracy was detrermined by the size of the discretization error estimated from the difference between analytical solution and numerical approximations. The results obtained are in good agreement with the exact solution. This work affirms that numerical methods give approximate solutions with less rigorous work and time as there is room for flexibility in terms of using different step sizes with the Euler solver as most accurate.

Open Access Original Research Article

Stability Analysis of Perturbed Linear Non-integer Differential Systems

Ubong D. Akpan

Journal of Advances in Mathematics and Computer Science, Page 24-29
DOI: 10.9734/jamcs/2021/v36i630370

In this work, the effect of perturbation on linear fractional differential system is studied. The analysis is done using Riemann-Liouville derivative and the conclusion extended to using Caputo derivative since the result is similar. Conditions for determining the stability and asymptotic stability of perturbed linear fractional differential system are given.