Lamees K. Alzaki

Bio: Lamees K. Alzaki is an academic researcher from Thi Qar University. The author has contributed to research in topics: Dominating set & Nonlinear system. The author has an hindex of 2, co-authored 2 publications receiving 6 citations.

The approximate analytical solutions of nonlinear fractional ordinary differential equations

Abstract: The Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper.The current technique incorporates two notable strategies in particular Sumudu transform (ST) and homotopy perturbation method (HPM). The proposed method’s hybrid property decreases the number of the quantity of computations and materials needed. In this method, illustration examples evaluate the accuracy and applicability of the mentioned procedure. The outcomes got by FSHPM are in acceptable concurrence with the specific arrangement of the problem.

Stability of (1,2)-total pitchfork domination

Abstract: Let $G=(V, E)$ be a finite, simple, and undirected graph without isolated vertex. We define a dominating $D$ of $V(G)$ as a total pitchfork dominating set, if $1leq|N(t)cap V-D|leq2$ for every $t in D$ such that $G[D]$ has no isolated vertex. In this paper, the effects of adding or removing an edge and removing a vertex from a graph are studied on the order of minimum total pitchfork dominating set $gamma_{pf}^{t} (G)$ and the order of minimum inverse total pitchfork dominating set $gamma_{pf}^{-t} (G)$. Where $gamma_{pf}^{t} (G)$ is proved here to be increasing by adding an edge and decreasing by removing an edge, which are impossible cases in the ordinary total domination number.

A Theory of Graphs

Abstract: A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

A new technique of reduce differential transform method to solve local fractional PDEs in mathematical physics

Abstract: In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising in mathematical physics with local fractional derivative operators (LFDOs). To get approximate solutions of these equations, we utilize the reduce differential transform method (RDTM) which is based upon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. The obtained solutions show that the present method is an efficient and simple tool for solving the linear and nonlinear PDEs within the LFDOs.

Time-Fractional Differential Equations with an Approximate Solution

Abstract: This paper shows how to use the fractional Sumudu homotopy perturbation technique (SHP) with the Caputo fractional operator (CF) to solve time fractional linear and nonlinear partial differential equations. The Sumudu transform (ST) and the homotopy perturbation technique (HP) are combined in this approach. In the Caputo definition, the fractional derivative is defined. In general, the method is straightforward to execute and yields good results. There are some examples offered to demonstrate the technique's validity and use.

Fuzzy equality co-neighborhood domination of graphs

Abstract: In that paper the fuzzy equality co-neighborhood domination and denoted by $gamma_{en}(G)$ for a new definition of domination was described for the fuzzy graph. This new definition was studied in a strong fuzzy graph and constraints were found for many several graphs. Complementary strong fuzzy graphs of the same graphs were examined and studied in detail.

An inverse triple effect domination in graphs

Abstract: In this paper, an inverse triple effect domination is introduced for any finite graph $G=(V, E)$ simple and undirected without isolated vertices. A subset $D^{-1}$ of $V-D$ is an inverse triple effect dominating set if every $v in D^{-1}$ dominates exactly three vertices of $V-D^{-1}$. The inverse triple effect domination number $gamma_{t e}^{-1}(G)$ is the minimum cardinality over all inverse triple effect dominating sets in $G$. Some results and properties on $gamma_{t e}^{-1}(G)$ are given and proved. Under any conditions the graph satisfies $gamma_{t e}(G)+gamma_{t e}^{-1}(G)=n$ is studied. Lower and upper bounds for the size of a graph that has $gamma_{t e}^{-1}(G)$ are putted in two cases when $D^{-1}=V-D$ and when $D^{-1} neq V-D .$ Which properties of a vertex to be belongs to $D^{-1}$ or out of it are discussed. Then, $gamma_{t e}^{-1}(G)$ is evaluated and proved for several graphs.