In this paper, we investigate and study a new subclass of meromorphic univalent functions defined by Rafid operator. We obtain coefficient inequalities, growth and distortion theorems, extreme points and closure theorems.

By means of Caputo $k-$fractional derivatives, in this work, we obtain new extensions of the Hermite-Hadamard inequality for modified $(h,m)-$ convex functions of the second type. At work, we show that some known results from the literature can be obtained as particular cases of the results presented here.

Let $X$ be a continuum and $n\in \mathbb{N}$, $F_n(X)$ denotes the hyperspace of all subsets of $X$ with at most $n$ points. Given $m,n\in \mathbb{N}$ with , we consider $S{F}_m^n(X)$ as the quotient space $F_n(X)/F_m(X)$. In this paper we will show that $S{F}_m^n(-)$ is a homotopic functor. Thus we will obtain a classification by homotopy. We will study the homotopy type of $S{F}_1^2(X)$ and we will calculate the Euler characteristic of $S{F}_m^n(X)$, when $X$ is a finite graph. Finally, we define a polynomial associated with a finite graph to give particular solutions to the problem: Given $m,n\in \mathbb{N}$, with , if $X$ a continuum such that $S{F}_m^n(X)$ is homeomorphic to $F_n(X)$, is $X$ contractible?

This paper presents the derivation of a new operational matrix of Caputo fractional derivatives through Hermite polynomials with Tau method to solve a set of fractional differential equations (FDEs). The proposed algorithm is intended to solve linear type of FDEs with the pre-defined conditions into a matrix form for redefining the complete problem as a system of a algebraic equations. The proposed strategy is then applied to solve the simplified FDEs in linear form. To assess the performance of the proposed method, exact and approximate solutions for a number of illustrative examples are obtained which prove the effectiveness of the idea.

We obtain the Lipschitz boundedness for a class of fractional multilinear integral operators $I_{\mathrm{\Omega },\alpha }^{A,m}$ with rough kernels $\mathrm{\Omega }\in L_s({𝕊}^{n-1})$, on the variable exponent local generalized Morrey spaces $M_{p(·),\phi }^{\left\{x_0\right\}}$, variable exponent generalized Morrey spaces $M_{p(·),\phi }$ and variable exponent vanishing generalized Morrey spaces $V{M}_{p(·),\phi }$, where the functions $A$ belong to homogeneous Lipschitz space ${\dot{\mathrm{\Lambda }}}_{\beta }$, $0\le \beta \le 1$.

Inspired by numerous studies on the difference analogues of the Bruck's conjecture, in this paper, we demonstrate the uniqueness of non-constant polynomial and a difference differential polynomial, both generated by a non-constant meromorphic function $g$, when they share a small function with finite weight. Our findings build upon and generalize a recent result of Chakraborty. [4]

In this paper we study the iterative system of nonlinear two-point tempered fractional order boundary value problems. By means of Krasnoselskii’s fixed point theorem on cone, some existence results of positive solutions are obtained. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind. Further, we study the existence of unique solution by an application of Rus’s theorem and Hyers-Ulam stability of the adderessed problem for $\ell =1$.

The objective of present paper is to introduce certain fixed point results for newly defined orthogonal generalized $F$-contraction mapping in the context of orthogonally modular metric spaces. Thus, several results are generalized and improved existing in the literature. We present some examples to show the validity and superiority of our results using graphs. Finally applications of our findings, show the existence of a unique solution of integral equation which make effective the new concepts and results.