Search

In this paper, we discuss the phenomenon of miscible flow with longitudinal dispersion in porous media. This process simultaneously occur because of molecular diffusion and convection. Here, we analyze the governing differential equation involving Caputo-Fabrizio fractional derivative operator having non singular kernel. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. We apply Laplace transform and use technique of iterative method to obtain the solution. Few applications of the main result are discussed by taking different initial conditions to observe the effect on derivatives of different fractional order on the concentration of miscible fluids.

In this paper we construct some new reproducing kernel functions in the reproducing kernel Sobolev space. These functions are new in the literature. We can solve many problems by these functions in the reproducing kernel Sobolev spaces.

In this paper, we obtain ostrowski type inequalities for exponentially convex function and exponentially s-convex function in second sense. Applications to some special means are also obtain. Here we extend the results of some previous investigations.

In this paper, some properties of soft radical of a soft int-ideal have been developed and soft prime int-ideal, soft semiprime int-ideal of a ring are defined. Several characterizations of soft prime (soft semiprime) int-ideals are investigated. Also it is shown that the direct and inverse images of soft prime (soft semiprime) int-ideals under homomorphism remains invariant.

Based on the conformable derivative, a generalized model of the Ambartsumian equation is analyzed in this paper. The solution is expressed as a power series of arbitrary powers. In addition, the convergence of the obtained series solution is theoretically proven. Furthermore, it is shown that the current series reduces to the corresponding one in the literature as the conformable derivative tends to one. It is also revealed that the obtained results are of acceptable accuracy. It is found that the residuals tend to zero in specific sub-domains. The diagonal Pade approximants are implemented to extend the domain of converge to include the whole domain.

In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5. We show that there is not any invariant concurrent vector field on such spaces. Our results show that in these manifolds each invariant conformal vector field is Killing and every invariant projective field is affine. Also, the space of some other invariant geometric fields such as affine, Killing, and harmonic vector fields on the manifolds are determined.

In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to a new defined quantity, which can be considered as an average of average 2-row sums. The new formulas extend previous results using the row sums and the average 2-row sums of a nonnegative matrix. We also characterize the equality cases of the bounds if the matrix is irreducible and we provide illustrative examples comparing with the existing bounds.

In the paper, the authors find two explicit formulas and recover a recursive formula for generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

In this paper, we develop some integral transforms involving a product of Humbert and Bessel functions with a weight e-γx2. These integral transforms will be evaluated in terms of hypergeometric functions. Various transformation formulae are also evaluated in terms of Appell functions to complete this study. Some special cases of the evaluated integrals yield some infinite series of generalized hypergeometric and Appell functions. As application, one of our main results is investigated to give an expression of the Generalized Humbert-Gaussian beams (GHGBs) propagating through a paraxial ABCD optical system.

In this paper, we consider a nonlinear multi-term Caputo fractional differential equation with nonlinearity depending on the unknown function together with its lower-order Caputo fractional derivatives and equipped with Riemann-Stieltjes integro multipoint boundary conditions. The given problem is transformed to an equivalent fixed point problem, which is then solved with the aid of standard fixed point theorems to establish the existence and uniqueness results for the problem at hand. Examples are constructed for the illustration of the obtained results.

In this paper, we derive existence and uniqueness results for a coupled system of nonlinear third order ordinary differential equations equipped with nonlocal multi-point anti-periodic type coupled boundary conditions. Leray-Schauder alternative and Banach contraction mapping principle are the main tools of our study. Examples are constructed for illustrating the obtained results. Under appropriate conditions, our results correspond to the ones for an ant-periodic boundary value problem of nonlinear third order ordinary differential equations.

In this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.

The one dimension Legendre Wavelet is a numerical method to solve one dimension equation. In this paper Black-Scholes equation (B-S), that has applied via single asset American option and Heston Cox- Ingersoll- Ross equation (HCIR), as partial differential equations have been studied in the form of stochastic model at first. The Black-Scholes and Heston Cox- Ingersoll- Ross Stochastic differential equations (SDE) models are converted to partial differential equations with a basic lemma in stochastic differential equation which called Ito lemma including derivatives and integration calculus in stochastic differential equations. Multi-dimensional Legendre wavelets method is based upon the expanded properties of Legendre wavelets from high order that is utilized to reduce these equations in to a system of algebraic equations. In fact the properties of Legendre wavelets are leads to reduce the PDEs problems to solution the ODEs systems. To ability and efficiency of the proposed techniques, numerical results and comparison with the other numerical method named Adomian decomposition method (ADM) for different values of parameters are tabulated and plotted.

The class of L-contractive mappings was introduced by Cho [ 12 ]. In this paper, we provide some fixed point results for such mappings via a control function introduced by Jleli and Samet [ 14 ] in the class of partial metric spaces. Some illustrating examples are given.

In this paper, we prove the existence and uniqueness of a positive solution of nonlinear Hadamard fractional differential equations with integral boundary conditions. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

In this paper, we investigate the existence criteria of at least one positive solution to the three-point boundary value problems with coupled system of Riemann-Liouville type nonlinear fractional order differential equations. The analysis of this study is based on the well-known Schauder's fixed point theorem. Some new existence and multiplicity results for coupled system of Riemann-Liouville type nonlinear fractional order differential equation with three-point boundary value conditions are obtained.

Fixed point theory has been used very successfully to obtain properties of solutions of integral and integro-differential equations of the form $ x(t) = g(t) +\int^t_0 A(t-s) v(t, s, x(s))ds $ because under general conditions the integral term may map bounded sets of continuous functions into equi-continuous sets. But quadratic integral equations have a coefficient of the integral terms of the form $ f(t, x(t))\int^t_0 A(t-s)v(t, s, x(s))ds $ which destroys the compactness of the map. Investigators have resorted to deep solutions often involving measures of non-compactness and Darbo's fixed point theorem. In an effort to obtain some elementary approaches, in this paper we develop an apparently new technique by showing that by using progressive contractions we can show conditions under which the product of two contractions is a contraction. We focus on integro-differential equations and use direct fixed point mappings which convert Lipschitz conditions into progressive contraction conditions.

In this paper, we establish a new Lyapunov-type inequality for a differential equation involving left Riemann-Liouville and right Caputo fractional derivatives subject to Dirichlet-type boundary conditions.

In this paper, we present some similarity reductions of the short pulse equation(SPE) based on the direct similarity reduction method proposed by Clarkson and Kruskal. These similarity reductions have a more general form than those obtained by using the Lie group method. Especially, we obtain one new similarity reduction which can not be obtained by Lie group method. Furthermore, we derive one new exact analytic solutions by the method of undetermined coefficients.

In the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented. The local and global stability analysis of the proposed model is obtained when the basic reproduction reproduction number is less or greater than 1. To show the global stability of the fractional Zika model, we use the Lyapunov function theory in fractional environment. Further, we simulate the fractional Zika model to present the graphical results for different values of fractional order and model parameters.

In this paper, we introduce a new kind of generalized fractional integral boundary conditions and develop the existence theory for a fractional di erential equation involving generalized Caputotype fractional derivative equipped with these conditions. We also study the inclusion case of the given problem. Examples are constructed to demonstrate the application of the obtained results.

We define a gap function to measure the difference of two distinct prime ideals in a given number field. In this paper, we determine all quadratic fields and cyclotomic fields satisfying the condition: there exist two distinct prime ideals whose gap is 1.

In the paper, the authors establish some new inequalities of the Gruss type for conformable fractional integrals. These inequalities generalize some known results.

This paper deals with a nonlinear viscoelastic wave equation with strong damping. By the means of the interpolation inequalities and di erential inequality technique, we obtain a lower bound for blow-up time of the solution. This result extends our earlier work Peng et al. [Appl. Math. Lett., 76, 2018].

This paper provides a mathematical study for analyzing the dynamics of smoking with health education campaigns involved. The method of next generation matrix is used to derive the basic reproduction number $R_0$. We prove that the smoking-free equilibrium is both locally and globally asymptotically stable if $R_0 < 1$; and the smoking-present equilibrium is globally asymptotically stable if $R_0 > 1$. By comparing with smoking dynamics without health education involved, we conclude that health education can decrease smoking population. Numerical simulations are used to support our conclusions.

In this paper we extend the tuberculosis epidemic model from a deterministic frameworkto a deterministic model with immunue response and after to stochastic one. We formulate it asa stochastic di erential equation. We, then, etablish the stabilities of di erent equilibria, and giveconditions for extinction and persistence of the desease.

In this paper, we introduce certain new subclasses of multivalent spirallike Bazilevicfunctions by using the concept of k-uniformly starlikness and k-uniformly convexity. We proveinclusion relations, su cient condition and Fekete-Szego inequality for these classes of functions.Convolution properties for these classes are also discussed.

In this paper, a SOR-like alternating variable method for computing the global solution of the maximal correlation problem is presented. The monotone convergence of the SOR-like alternating variable method is proved. Numerical experiments show the effciency of our method.

Let F : R → R be a generalized derivation of a 2-torsion free prime ring R together witha derivation d: In this paper, we show that a nonzero Jordan ideal J of R contains a nonzero ideal ofR. Further, we use this result to prove that if F([x,y]) ∈ Z(R) for all x, y ∈ J; then R is commutative.Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.

In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation with high contrast, studied together with a corresponding multiscale method in (Ohlberger, Verf\"urth. A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast, arXiv:1605.03400, 2016). There, an unavoidable resolution condition on the mesh sizes in terms of the wave number has been observed, which is known as "pollution effect" in the finite element literature. Following ideas of (Gallistl, Peterseim. Comput. Methods Appl. Mech. Engrg. 295:1-17, 2015), we use standard finite element functions for the trial space, whereas the test functions are enriched by solutions of subscale problems (solved on a finer grid) on local patches. Provided that the oversampling parameter $m$, which indicates the size of the patches, is coupled logarithmically to the wave number, we obtain a quasi-optimal method under a reasonable resolution of a few degrees of freedom per wave length, thus overcoming the pollution effect. In the two-scale setting, the main challenges for the LOD lie in the coupling of the function spaces and in the periodic boundary conditions., Comment: 20 pages

The paper deals with the regularity criteria for the weak solutions to the 3D Boussinesq equations in terms of the partial derivatives in Besov spaces. It is proved that the weak solution $$(u,\theta )$$ becomes regular provided that $$\begin{aligned} (\nabla _{h}{\widetilde{u}},\nabla _{h}\theta )\in L^{1}(0,T;\overset{\cdot }{B }_{\infty ,\infty }^{0}({\mathbb {R}}^{3})) \end{aligned}$$Our results improve and extend the well-known result of Dong and Zhang (Nonlinear Anal 11:2415–2421, 2010) for the Navier–Stokes equations.

In this paper, logarithmically improved regularity criteria for the Boussinesq equations are established under the framework of Besov space $\overset{.}{B}_{\infty ,\infty }^{-r}$. We prove the solution $(u,\theta )$ is smooth up to time $T>0$ provided that \begin{equation} \int_{0}^{T}\frac{\left\Vert u(\cdot ,t)\right\Vert _{\overset{.}{B} _{\infty ,\infty }^{-r}}^{\frac{2}{1-r}}}{\log (e+\left\Vert u(t,.)\right\Vert _{\overset{.}{B}_{\infty ,\infty }^{-r}})}dt

It is well-known that under suitable conditions there exists a unique solution of a ddimensional linear stochastic differential equation. The explicit expression of the solution, however, is not given in general. Hence, numerical methods to obtain approximate solutions are useful for such stochastic di erential equations. In this paper, we consider stochastic difference equations corresponding to linear stochastic differential equations. The difference equations are constructed by weakly dependent random variables, and this formulation is raised by the view points of time series. We show a convergence theorem on the stochastic difference equations.

In this paper, for a given matrix $A=(a_{ij}) \in \mathbb{C}^{n\times n}$, in terms of $r_i$ and $c_i$, where $ r_i = \sum\limits_{j = 1,j \ne i}^n {\left| {a_{ij} } \right|}, \ \ c_i = \sum\limits_{j = 1,j \ne i}^n {\left| {a_{ji} } \right|} $, some new inclusion sets for singular values of a matrix are established. It is proved that the new inclusion sets are tighter than the Gersgorin-type sets [1] and the Brauer-type sets [2]. A numerical experiment show the efficiency of our new results.

In this paper, we introduce a new subclass of multivalent functions associated with conic domain in an open unit disk. We study some convolution properties, su cient condition for the functions belonging to this new class.

In this paper, we will establish a sufficient condition for the regularity criterion to the 3D MHD equation in terms of the derivative of the pressure in one direction. It is shown that if the partial derivative of the pressure $\partial _{3}\pi $ satisfies the logarithmical Serrin type condition $\partial _{3}\pi $ satisfies the logarithmical Serrin type condition \begin{equation*} \int_{0}^{T}\frac{\left\Vert \partial _{3}\pi (s)\right\Vert _{\overset{% \cdot }{\mathcal{M}}_{2,\frac{3}{r}}}^{\frac{2}{2-r}}}{1+\ln (1+\left\Vert b(s)\right\Vert _{L^{4}})}ds