Open Journal of Mathematical Sciences (OMS)

This paper investigates the existence results and uniqueness of solutions for a class of boundary value problems for fractional differential equations with the Hilfer fractional derivative. The reasoning is mainly based upon Mönch’s fixed point theorem associated with the technique of measure of noncompactness. We illustrate our main findings, with a particular case example, included to show the applicability of our outcomes. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions.

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

The concept of weak implicative UP-filters in UP-algebras is introduced and analyzed. Some characterizations of weak implicative UP-filters are derived with the using of some other filter types in such algebras.

This paper introduces the concept of homomorphism in intuitionistic fuzzy multigroups context. It also investigates Some homomorphic properties of intuitionistic fuzzy multigroups. It is shown that the homomorphic image and homomorphic preimage of intuitionistic fuzzy multigroups are also intuitionistic fuzzy multigroups. Finally, it presents some homomorphic properties of normalizer of intuitionistic fuzzy multigroups.

The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.

In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.

In this article, authors discussed the existence of solution of non-linear diophantine equation \({379}^x+{397}^y=z^2,\) where \(x,y,z\) are non-negative integers. Results show that the considered non-linear diophantine equation has no non-negative integer solution.

This paper provides a procedure for estimating Stochastic Volatility (SV) in financial time series via latent autoregressive in a Bayesian setting. A Gaussian distributional combined prior and posterior of all hyper-parameters (autoregressive coefficients) were specified such that the Markov Chain Monte Carlo (MCMC) iterative procedure via the Gibbs and Metropolis-Hasting sampling method was used in estimating the resulting exponentiated forms (quadratic forms) from the posterior kernel density. A case study of Naira to eleven (11) exchangeable currencies’ rates by Central Bank of Nigeria (CBN) was subjected to the estimated solutions of the autoregressive stochastic volatility. The posterior volatility estimates at 5%, 50%, and 95% quantiles of \({e^{\frac{\mu }{2}}}\) = (0.130041, 0.1502 and 0.1795) respectively unveiled that the Naira-US Dollar exchange rates has the highest rates bartered by fluctuations.

The theory of multigroups is a generalized group’s theoretic notions in multiset framework. Although myriad of researches have been done in multigroup theory, but some group’s analogue concepts have not been investigated in multigroup setting. In this paper we propose the notions of divisible and pure multigroups and characterize some of their properties. It is established that the image and preimage of homomorphism of divisible and pure multigroups are divisible and pure multigroups. The nexus between divisible and pure multigroups and that of divisible and pure groups are instituted using the concept of cuts of multigroups.

In this paper, we have established a theorem involving a pair of mappings satisfying a weakly contraction type condition in the context of quasi \(\alpha\)b-metric space and proved the existence and uniqueness of coupled coincidence and coupled common fixed points. The concept of weakly compatibility of the pair of maps is applied to show the uniqueness of coupled common fixed point. This work offers an extension to the published work of Nurwahyu and Aris [1].