The nonlinear conformable time-fractional modified Camassa-Holm (MCH) equation plays an important role in physics. It is an interesting model to define change waves with weak nonlinearity. The aim of this study is to present the new exact solutions of conformable time-fractional MCH equation. For this purpose, an effective method which is the Improved Bernoulli Sub-Equation Function Method (IBSEFM) has been used. The 2D and 3D graphs and contour surfaces acquired from the values of the solutions are plotted by the aid of mathematics software. The obtained results confirm that IBSEFM is a powerful mathematical tool to solve nonlinear conformable time-fractional partial differential equations arising in mathematical physics.
It is shown that the following $\left( k+l\right) $-order nonlinear difference equation $$x_{n}=\frac{x_{n-k}x_{n-k-l}}{x_{n-l}\left( a_{n}+b_{n}x_{n-k}x_{n-k-l}\right)}, \ n\in \mathbb{N}_{0},$$ where $k,l\in \mathbb{N}$, $\left(a_{n} \right)_{n\in \mathbb{N}_{0}}$, $\left(b_{n} \right)_{n\in \mathbb{N}_{0}}$ and the initial values $x_{-i}$, $i=\overline {1,k+l}$, are real numbers, can be solved and extended some results in literature. Also, by using obtained formulas, we give the forbidden set of the initial values for aforementioned equation and study the asymptotic behavior of well-defined solutions of above difference equation for the case $k=3$, $l=k$.
In this article, the author used Mellin and Kontorovich-Lebedev transforms to establish certain integrals involving Macdonald's functions. Transform method is a powerful tool for solving singular integral equations, evaluation of certain integrals and solution to partial differential equations. The result reveals that the transform method is very convenient and effective.
The purpose of this study is to present a new modification of finite difference method (FDM) for approximating the solution of the two-interval boundary value problems for second order differential equations, whose main feature is the nature of the imposed conditions. Namely, the investigated problems contains not only boundary conditions at the points of the considered interval, but also an additional conditions at one interior point of interaction, so-called transmission conditions. Naturally, the analysis of two-interval boundary-value problems is more complicated and it is not clear how to extend the classical FDM to such type problems. The proposed modification of FDM tested on two model problems with known exact solutions. The obtained result are illustrate the applicability and efficiency of our own algoritm, which can be readily extended to all many-interval problems.
In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution.
In the present article, the author investigates some properties of fractional analytic function g(m) (z)(alpha), belonging to two new subclasses of m-fold symmetric starlike and convex functions in the open unit disk. In addition, properties of certain new subclass T-m,n(alpha)(beta), of m-fold symmetric bi-Bazilevic functions associated with modified sigmoid functions are considered while several other corollaries follow as simple consequences.
In this article, the truncated exponential polynomials are taken as base with the Gould-Hopper polynomials to introduce a hybrid family of truncated exponential-Gould-Hopper polynomials. These polynomials are framed within the context of monomiality principle and their properties are established. Certain properties including operational representations, expansion formula, integral representation and summation formula are also derived for this family. Further, the graphs of these polynomials are drawn for different values of indices using MATLAB.
Motivated by the work of J. S\'andor [19], in this paper we establish a new Wilker type and Huygens type inequalities involving the trigonometric and hyperbolic functions. Moreover, in terms of hyperbolic functions, the upper and lower bounds of sin(x)/x and tan(x)/x are given.
This paper studies the fourth-order problem with multi-term time fractional integral operator under simply supported type conditions. We first introduce a novel computational approach, the discrete singular convolution (DSC) algorithm, for analyzing this problem. Detailed discrete formulations and the treatment of simply supported boundary condition are established. We provide some numerical results to demonstrate the validity and applicability of the proposed technique. Comprehensive comparisons are given based on a variety of time increment, grid spacing and wave number. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that the DSC algorithm is an accurate, stable and robust approach for solving the fourth-order integro-differential equation with multi-term time fractional integral operator.
This paper aims to obtain exact and numerical solutions of the nonlinear Benjamin Bona Mahony-Burgers (BBM-Burgers) equation. Here, we propose the modified Kudryashov method for getting the exact traveling wave solutions of BBM-Burgers equation and a septic B-spline collocation finite element method for numerical investigations. The numerical method is validated by studying solitary wave motion. Linear stability analysis of the numerical scheme is done with Fourier method based on von-Neumann theory. To show suitability and robustness of the new numerical algorithm, error norms $L_{2}$, $L_{\infty }$ and three invariants $I_{1},I_{2}$ and $I_{3}$ are calculated and obtained results are given both numerically and graphically. The obtained results state that our exact and numerical schemes ensure evident and they are penetrative mathematical instruments for solving nonlinear evolution equation.
The main objective of this paper is to establish several new lower and upper bounds for the functions sinh x/x and cosh x. Following the simple approach, our results give refinements and generalizations of some known inequalities involving these functions.
In this work, we construct vector spaces $l_{p}\left( \mathbb{BC}\left(N\right) \right) $ of absolutely $p-$ summable $\ast -$bicomplex sequences with the $\ast -$ norm $\overset{..}{\parallel }.\overset{..}{\parallel }_{2,l_{p}\left( \mathbb{BC}\left( N\right) \right) }$ over the field $\mathbb{C}\left( N\right).$ Also, we show that some inclusion relations hold and these vector spaces are Banach spaces by using Minkowski's inequality in $\mathbb{BC}\left( N\right) $ with respect to $\overset{..}{\parallel }.\overset{..}{\parallel }_{2}.$
In 1940, P. Hall introduced the concept of isoclinism of groups. Heidarian et al. studied the concept of n-isoclinism of pairs of groups. In this paper, we investigate the concept of n-isoclinism between two pairs of groups and give some relations between the notions of n-isoclinism of groups and n-isoclinism of pairs of groups.
In this paper we have discussed about second Hankel determinant of Ma-Minda starlike bi-univalent and Ma-Minda convex bi-univalent functions in the open unit disc Delta subordinate to a starlike univalent function whose range is symmetric with respect to the real axis involving the Fekete-Szego parameter lambda.
Let F-3d is the finite field of order 3(d) with d be a positive integer, we consider A(4) := F-3d [epsilon] = F-3d [X]/(X-4) is a finite quotient ring, where epsilon(4) = 0. In this paper, we will show an example of encryption and decryption. Firstly, we will present the elliptic curve over this ring. In addition, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. Precisely, we give a numerical example of cryptography (encryption and decryption) by using two methods with a secret key.
In this paper, we deal with meromorphic functions and its kth derivative. We consider a set of roots of unity, which shares the functions of the form (fnP(f))(k) and (gnP(g))(k) and obtain uniqueness results which improves the results of V. H. An and H. H. Khoai. Also, by introducing the concept of weighted sharing, we obtain analogous results from these authors.
We consider a coupled viscoelastic plate nonlinear equations with degenerate damping terms on a bounded domain in Rn. We establish the global existence results under different conditions.
In this paper, we investigate the uniqueness of meromorphic functions sharing a set with counting multiplicity and also with weight 1 in an angular domain.
