In this paper, we aim to study some algebraic properties of generalized bicomplex number. We also give the definitions of the generalized bicomplex Polynomial, generalized bicomplex exponential function and Generalized bicomplex cosine and sine function in order to establish our subsequent study.
The aim of this paper is the characterization of biharmonic curves in the $3-$ dimensional Lorentz-Heisenberg group $\mathcal{H}_{3}$ endowed with a left invariant Lorentzian metric $g_{i}$ in the two following cases: \begin{enumerate} \item $g_{1}=-dx^{2}+dy^{2}+(xdy+dz)^{2},$ \item $g_{2}=dx^{2}+dy^{2}-(xdy+dz)^{2}.$ \end{enumerate}
This work is concerned with the construction of minimal and maximal solutions for a class of quasilinear fourth order impulsive differential equation with integral boundary conditions, where the nonlinearity is a continuous function depending on the second and third derivative of the unknown function. We also give an example to illustrate our results.
The Klein 4-group, denoted by $V_4$ is an abelian group of order 4. It has elements $V_4 =\{0, a, b, c\},$with $a+a=b+b=c+c=0$ and $a+b=c,b+c=a,c+a=b.$ A graph $G = (V (G),E(G)),$ withvertex set $V(G)$ and edge set $E(G),$ is said to be $star$ magic if there exists a labeling $f:V(G)\rightarrow V_4\backslash\{0\}$ such that the induced mapping $V_f^+:V(G)\rightarrow V_4$ defined by $V_f^+(v)=\sum_{u\in N(v)} f^*(uv),$ where $f^*(uv)=f(u)+f(v)$ is a constant map. If this constant is $p,$ where $p$ is any non zero element in $V_4$, then we say that $f$ is a $p-star$ magic labeling of $G$ and $G$ is said to be a $p-star$ magic graph. If this constant is $0,$ then we say that $f$ is a $0-star$ magic labeling of $G$ and $G$ is said to be a $0-star$ magic graph.
In this article, we use the classical fixed point theorems to prove the main results for the integral boundary value problem for Hilfer-Katugampola fractional differential equations. An Example is presented to clarify the main results at the end .
This paper deals with fractional model of Bloch equation in Nuclear Magnetic Resonance (NMR). The applications of NMR are magnetic resonance imaging (MRI) for medical diagnosis, magnetic resonance microscopy (MRM) in research settings, chemists can determine the structure of many compounds and for analysing expansive biological samples like nucleic acids, RNA, DNA and proteins. Here, we present a numerical algorithm using Chebyshev polynomial of third kind for the numerical solution of integer and fractional order Bloch equation. Entire trajectory of magnetization is shown in 3D for integer and fractional order Bloch equation. The dynamic of magnetization is also shown for integer and fractional order relaxation. Obtained numerical results are simulated with known solutions. We also compared results with known solutions. Errors tables are used to show the accuracy of the method.
In this paper, we introduce King type modification of composition of SzAisz-Mirakyan and Durrmeyer-Chlodowsky operators. Rate of convergence is given in the frame of weighted space. Furthermore, we proved a Voronovskaja type theorem for these operators.
In this paper we discuss about the solution of abstract fractional integro differential equations with different conditions on the operator A. The solution obtained by using Mittag-Leffler function is correct when the operator A is bounded. However when the operator A is unbounded the representation derived in [1] seems to be incorrect. We also obtain a suitable form of solution to stochastic fractional differential equation with unbounded operators.
Let T be a time scale not bounded below and above such that t₀∈T. In this paper, we provide new sufficient conditions and use the Banach fixed point theorem to establish the stability results about the zero solution for the following Levin-Nohel intego-dynamic equation with variable delay x^{I”}(t)+∫_{t-r(t)}^{t}a(t,s)x(s)I”s+(g(t,x(t-r(t))))^{I”}=0, t∈[tâ‚€,∞)∩T, where x^{I”} is I”-derivative on T. An asymptotic stability theorem with a necessary and sufficient condition is proved. In addition, the case of the equation with several delays is studied. The results obtained here extend the work of Bessioud, Ardjouni, Djoudi b0 .
In this work we investigate a tri-trophic food chain model in pres- ence of weak Allee effect in the prey population. At first, we observe the dynamics of our model system for variation of half-saturation constant b_1 and investigate the nonlinear phenomena such as stable focus, limit cycle oscillation, period-doubling and nally chaos. Then we have tried to control the chaotic dynamics of the original system by introducing weak Allee effect in the prey species. We have also derived the criteria for local stability and instability of model system around the biological feasible equilibria. We have discussed the different conditions for the coexistence of equilibrium solutions. We have noticed that chaotic dynamics can be prevented by introducing weakAllee effect.
Rakotch contractions as well as the Matkowski fixed point theorem are used in order to obtain generalised fractal interpolation functions with extensive practical applications. In particular, our previous work on bivariable fractal interpolation functions is extended by offering a more comprehensive overview.
In this paper, we apply the fixed point theorems in cones to find the positive solutions of boundary value problems for nonlinear fractional impulsive differential equations with p-Laplacian operator, and involving both the left and the right Caputo fractional derrivatives.
An unsteady boundary layer analysis for the mingled impacts of radiation and viscous dissipation in a laminar free convective stream past an upright inclined infinite plate with constant wall heat flux is presented. The altered dimensionless periphery layer equations of the flow are coupled and nonlinear PDE’s , the resultant transformed equations are evaluated by employing an unconditionally stable, implicit finite difference method as discussed by Crank–Nicolson. A parametric analysis demonstrating the persuade of sundry pertinent parameters like $ \epsilon $, $ Pr $ and $Rd$ are executed and numerical outcomes for translational momentum and temperature near the periphery layer are conferred and presented graphically for the parametric variations.
The main aim of this manuscript is to analyze the existence of piecewise-continuous mild solution of Atangana-Baleanu fractional integro-differential systems with non-instantaneous impulses in Banach space. Based on the Banach contraction principle fixed point theorem joined with $\rho$-resolvent operators, we develop the main results. In the end, an example is given to justify the theoretical results.
To examine different latent characteristics of a given time series several methods are available. Here we have used Multifractal Detrended Fluctuation Analysis (MFDFA) method for the analysis of YES bank time series of closing prices from the duration of 9th July 2014 to 9th April 2020. We found that during period of crisis, time series is extremely multifractal and consequently the strength of multifractality also increases and reaches close to unity. We also observe decrease in efficiency during this period. We therefore, conclude that multifractality can be used as one of the parameter for prediction of stability of banking sector.
This article deals with idea of piecewise stepanov-like almost automorphic solution to fractional Fredholm-Volterra integro differential equation with impulsive condition. First we demonstrate existence of such solution by using fixed point theorem and analyse the stability of the solution. An example is provided to outline the thought developed on this work.
We proposed and analyzed a predator-prey model where the prey population was not only infected through contact but also got infection from external sources. In this paper we also considered the allee effect in the susceptible prey population. Time delay effect is an important component in every biological systems and cannot be ignored. The present paper investigate to observe the quantitative and qualitative behavior of the system with gestation delay. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate, there exists several critical values of delay factor below and above which system is stable and unstable alternatively. It is also observed that delay prevents the extinction of predator population and outbreak of disease. Finally we observe that the instability arising from the gestation delay may be controlled if somehow the growth rate of predator population and external source of infection increaseand predation rate for infected prey decreases. We have also observed that allee will drive all prey species in extinction but delay will save these population from extinction. It is concluded that delay has important role in saving the prey population from extinction.
We prove existence and regularity of solutions to the following problem, defined by a class of monotone operators with singular nonlinearity\begin{equation*}\left\{\begin{array}{c}-div(a(x,Du))+\nu\left \vert u \right \vert^{p-2}u=\dfrac{f}{u^{\gamma(x)}}%\text{ in }\Omega \\ u>0\text{ in }\Omega \\u=0\text{ on }\partial{\Omega}\end{array}%\right.\end{equation*}where $\Omega$ is a bounded open set in $%%TCIMACRO{\U{211d} }%%BeginExpansion\mathbb{R}%EndExpansion^{N},1 0$ is a smooth function,having a convenient behavior near $\partial{\Omega}$ and $\nu>0$ is a real number and $f$ is a non-negative function belonging to some Lebesgue space $L^m(\Omega)$.
We consider a nonlinear damped Porous system subjected to a nonlinear delayed damping acting on the volume fraction equation. Namely, we investigate the following system \begin{equation*} \begin{dcases} \rho_1 u_{tt}(x,t) - \kappa u_{xx}(x,t)- b \phi_x(x,t) =0 , \\ \rho_2 \phi_{tt}(x,t) - \delta \phi_{xx}(x,t) + b u_{x}(x,t) + \xi \phi(x,t) + \mu_1 g_1( \phi_t(x,t)) + \mu_2 g_2( \phi_t(x,t-\tau ))=0\end{dcases}\end{equation*} together with Dirichlet-Dirichlet boundary conditions in $[0,1] \times [0,+\infty[$. By the classical Faedo-Galerkin procedure, we first prove the well-posedness of solutions without paying attention on the weights of feedbacks (delayed or not). This improves many earlier results existing in the literature by removing the usual restrictions imposed on $\mu_1$ and $\mu_2$. Furthermore, by applying the multiplier method integrated with some properties of convex functions, we establish two general decay estimates with rates that depend on the speeds of wave propagation and the smoothness of the initial data
