Abstract: In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove the existence of a unique solution and investigate the continuous dependence of the solution upon the initial data and two types of Ulam stability: Ulam-Hyers and Ulam-Hyers-Rassias ones. Then, we give an example to illustrate the main results. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems. Our technique based on the method of finite difference approximations. We obtain a quadratic order accurate an explicit method using the set of initial conditions in a natural way and approximations for the approximate numerical solution after the discretization of the continuous problem under appropriate conditions. We discuss the development of the method and the periodic property of the solution of the problem. In the numerical experiment, we consider both linear and nonlinear model problems to test the efficiency and accuracy of the method. The tabulated numerical results in computational experiments approve the quadratic order accuracy and efficiency of the method. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: In this paper we show that, if that the function f : [0, ∞) → 𝔾 is operator monotone in [0, ∞) then there exist b ≥ 0 and a positive measure m on [0, ∞) such that [ f(B)-f(A) ](B-A)==b(B-A)2+∫0∞s2[ ∫01[ ((1-t)A+tB+s)-1(B-A) ]2dt ]dm(s)\matrix{ {\left[ {f\left( B \right) - f\left( A \right)} \right]\left( {B - A} \right) = } \hfill \cr { = b{{\left( {B - A} \right)}^2} + \int_0^\infty {{s^2}\left[ {\int_0^1 {{{\left[ {{{\left( {\left( {1 - t} \right)A + tB + s} \right)}^{ - 1}}\left( {B - A} \right)} \right]}^2}dt} } \right]dm\left( s \right)} } \hfill \cr } for all A, B > 0. Some necessary and sufficient conditions for the operators A, B > 0 such that the inequality f(B)B+f(A)A≥f(A)B+f(B)Af\left( B \right)B + f\left( A \right)A \ge f\left( A \right)B + f\left( B \right)Aholds for any operator monotone function f on [0, ∞) are also given. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The object of the present article is to study the notion of η-Einstein-like LP-Sasakian manifolds admitting η-Ricci soliton. Furthermore, we study the η-Ricci soliton on LP-Sasakian manifolds when the potential vector field V is point-wise collinear. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: Let 𝒜 p be the class of functions f of the form f(z)=zp+ap+1zp+1+ap+2zp+2+⋯f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} + \cdots that are analytic in the open unit disk 𝕌. For f ∈ 𝒜 p, new integral and differential operator nf is considered. The object of the present paper is to discuss some interesting properties of nf and to consider some examples for our results. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The aim of this paper is to give sufficient conditions for Ψ − conditional exponential asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The aim of this paper is to study a frictional contact problem between an elastic body and a foundation. We focus on the optimal control of the model which consists of acting with a control on a portion of the boundary of the body and leading the stress tensor as close as possible to a given target. We state an optimal control problem for which we establish an existence theorem of the solution. We then introduce a sequence of regularized problems depending on a positive parameter α and we study the convergence of the sequence of the solutions when the parameter α tends to zero. Finally, an optimality condition is established for this problem. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of this paper is to give two proofs of this important theorem and explore some of its numerous consequences. As an application, we compute the genus of some interesting algebraic curves or Riemann surfaces. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The L1and L2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms L2 and L∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs). PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: In this paper, we establish a fixed point theorem for generalized contraction mappings in b-metric spaces endowed with a digraph. As an application of this result, we obtain fixed points of cyclical mappings in the setting of b-metric spaces. Our results extend and generalize several existing results in the literature. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: In the present paper, some results on a Lorentzian Sasakian manifold endowed with a quarter-symmetric metric connection have been studied. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: In this paper we ensure that for some class of impulsive differential equations with delay the zero solution is asymptotically stable by means of fixed point theory. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: Some inequalities of Hermite-Hadamard type for GG-convex functions defined on positive intervals are given. Applications for special means are also provided. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: An L(3, 2, 1)-labeling of a graph G is an assignment f from the vertex set V (G) to the set of non-negative integers such that f (x) − f (y) ≥ 3 if x and y are adjacent, f (x) − f (y) ≥ 2 if x and y are at distance 2, and f (x) − f (y) ≥ 1 if x and y are at distance 3, for all x and y in V (G). The L (3, 2, 1)-labeling number k (G) of G is the smallest positive integer k such that G has an L (3, 2, 1)-labeling with k as the maximum label. In this paper, we consider banana trees of type 1, banana trees of type 2 and path-union of t-copies of the star K1,n and find the k-numbers of them. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: The object of the present paper is to study generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifolds whose metric tensor is η-Ricci soliton. The paper also aims to bring out curvature conditions for which η-Ricci solitons in Kenmotsu manifolds are sometimes shrinking or expanding and some other time remain steady. The existence of each generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifold is ensured by an example. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: Let f and g be two nonconstant meromorphic functions sharing two finite sets, namely S ⊂ ℂ and {∞}. We prove two uniqueness theorems under weaker conditions on ramification indices, reducing the cardinality of the shared set S and weakening the nature of sharing of the set {∞} which improve results of Fang-Lahiri [7], Lahiri [17], Banerjee -Majumder-Mukherjee [5] and others. PubDate: Mon, 21 Dec 2020 00:00:00 GMT

Abstract: One of the important problems in finite groups theory is group characterization by specific property. Properties, such as element orders, set of elements with the same order, the largest element order, etc. In this paper, we prove that the simple groups 2D8((2n)2)where, 28n+ 1 is a prime number are uniquely determined by its order and the largest elements order. PubDate: Mon, 21 Dec 2020 00:00:00 GMT