Arabian Journal of Mathematics最新文献

In this study, the theory of curves is reconstructed with fractional calculus. The condition of a naturally parametrized curve is described, and the orthonormal conformable frame of the naturally parametrized curve at any point is defined. Conformable helix and conformable slant helix curves are defined with the help of conformable frame elements at any point of the conformable curve. The characterizations of these curves are obtained in parallel with the conformable analysis Finally, examples are given for a better understanding of the theories and their drawings are given with the help of Mathematics.

Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely (P^{*}(n), M(n), T^{*}(n), L(n), K(n), A(n)), and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo (2^acdot 5^ell ) for (P^{*}(n)), modulo (2^3) for M(n) and (T^*(n)), where (a=3, 4) and (ell ge 1). For instance, we prove that for (nge 0),

In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki:

We study the asymptotic behavior of trajectories of the continuous dynamical system(CDS) associated with the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi (J Math Anal Appl 241:46–55, 2000). We establish that the trajectories x(t) of the continuous dynamical system (CDS) has an asymptotic behavior similar to the behavior of the sequences ((x_{n})) generated by the discrete viscosity approximation (DDS)

In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete (CAT_p(0)) metric spaces for (pge 2). Our results extend and improve many results in the literature.

In this article, we employ the group-theoretic methods to explore the Lie symmetries of the Klein–Gordon–Zakharov equations, which include time-dependent coefficients. We obtain the Lie point symmetries admitted by the Klein–Gordon–Zakharov equations along with the forms of variable coefficients. From the resulting symmetries, we construct similarity reductions.The similarity reductions are further analyzed using the power series method/approach and furnished the series solutions. Additionally, the convergence of the series solutions has been reported.

The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms (K_{s}(varepsilon )). We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of (xi ). Moreover, we acquire Chen-Ricci inequalities on the (ker vartheta _{*}) and ((ker vartheta _{*})^{bot }) distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of (xi ).

This paper deals with some existence and uniqueness results for a class of deformable fractional differential equations. These problems encompassed nonlinear implicit fractional differential equations involving boundary conditions and various types of delays, including finite, infinite, and state-dependent delays. Our approach to proving the existence and uniqueness of solutions relied on the application of the Banach contraction principle and Schauder’s fixed-point theorem. In the last section, we provide different examples to illustrate our obtained results.

Of concern is a Cohen–Grossberg neural network (CGNNs) system taking into account distributed and discrete delays. The class of delay kernels ensuring exponential stability existing in the previous papers is enlarged to an extended class of functions guaranteeing more general types of stability. The exponential and polynomial (or power type) type stabilities becomes particular cases of our result. This is achieved using appropriate Lyapunov-type functionals and the characteristics of the considered class.

This paper investigates some well-posedness issues of the fractional inhomogeneous Schrödinger equation

where (0<gamma <1) and (rho <0). Here, one considers the inter-critical regime (0<s_c:=frac{N}{2}-frac{2gamma +rho }{p-1}<gamma ), where (s_c) is the energy critical exponent, which is the only one real number satisfying (Vert kappa ^frac{2gamma +rho }{p-1}u_0(kappa cdot )Vert _{dot{H}^{s_c}}=Vert u_0Vert _{dot{H}^{s_c}}). In order to avoid a loss of regularity in Strichartz estimates, one assumes that the datum is spherically symmetric. First, using a sharp Gagliardo–Nirenberg-type estimate, one develops a local theory in the space (dot{H}^gamma cap dot{H}^{s_c}). Then, one investigates the (L^{frac{N(p-1)}{rho +2gamma }}) concentration of finite-time blow-up solutions bounded in (dot{H}^{s_c}). Finally, one proves the existence of non-global solutions with negative energy. Since one considers the homogeneous Sobolev space (dot{H}^{s_c}), the main difficulty here is to avoid the mass conservation law.