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Adem Kilicman

Publications and source records attributed to Adem Kilicman.

At least 19 recordsLinked to original sources
arXiv2024

A Fractional Model of Abalone Growth using Adomian Decomposition Method

This study is a modification of the McKendrick equation into a growth model with fractional order to predict the abalone length growth. We have shown that the model is a special case of Taylor's series after it was analysed using Adomian decomposition method and Caputo fractional derivative. By simulating the series with some fractional orders, the results indicate that the greater the fractional order of the model, the series values generated are greater as well. Moreover, the series that is close to the real data is the one with a fractional order of $0.5$. Therefore, the growth model with a fractional order provides more accuracy than a classical integer order.

math.GM↗
arXiv2024

The Problem of Split Equality Fixed-Point and its Applications

It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life, to address this issue, we studied the SEFPP involving the class of quasi-pseudocontractive mappings in Hilbert spaces and constructed novel algorithms in this regards, and we proved the algorithms' convergence both with and without prior knowledge of the operator norm for bounded and linear mappings. Additionally, we gave applications and numerical examples of our findings. A variety of well-known discoveries revealed in the literature are generalized by the findings presented in this work.

math.GM↗
arXiv2022

Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters

Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich operators generated by the basic q-calculus. More precisely, we study the convergence properties of our new operators in the space of continuous functions and Lebesgue space. We obtain the degree of convergence with the help of modulus of continuity and integral modulus of continuity. Furthermore, we establish the quantitative estimates of Voronovskaja-type.

math.GM↗
arXiv2021

On Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative with respect to time with $1<α<2$. The method of the energy inequalities is used to prove the existence and the uniqueness of solutions of the problem. The finite difference method is also introduced to study the problem numerically in order to find an approximate solution of the considered problem. Some numerical examples are presented to show satisfactory results.

math.NA↗
arXiv2021

Solitons of nonlinear dispersive wave steered from Navier-Bernoulli hypothesis and Love's hypothesis in the cylindrical elastic rod with compressible Murnaghan's materials

The nonlinear dispersive wave equation inside the cylindrical elastic rod is derived by applying the Navier-Bernoulli hypothesis and Love's relation in \cite{5}. The elastic rod is assumed to be composed of the Murnaghan's materials such as Lam$\acute{e}$'s coefficient, Poisson ratio and constitutive constant which are compressible in nature. In this research paper we apply the two integral architectures namely extended sine-Gordon method and modified exponential function method to study the dispersive wave and solved for the solitons and their classifications. The existence of the number of solutions are proved with respect to the linear equation obtained by balancing principle. The related two and three dimensional graphs are simulated and drawn to show the complex structures.

math-ph↗
arXiv2019

Integral inequalities for s-convexity via generalized fractional integrals on fractal sets

In this study, we establish a new integral inequalities of Hermite-Hadamard type for $s$-convexity via Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann-Liouville into a single form. We show that the new integral inequalities of Hermite-Hadamard type can be obtained via the Riemann-Liouville fractional integral. Finally, we give some applications to special means.

math.GM↗
arXiv2019

On Edge-Partitioning of Complete Geometric Graphs into Plane Trees

In response to a well-known open question ``Does every complete geometric graph on $2n\/$ vertices have a partition of its edge set into $n\/$ plane spanning trees?" we provide an affirmative answer when the complete geometry graph is in the regular wheel configuration. Also we present sufficient conditions for the complete geometric graph on $2n\/$ vertices to have a partition of its edge set into $n\/$ plane spanning trees (which are double stars, caterpillars or $ w\/$-caterpillars).

math.CO↗
arXiv2019

On Convex Graphs Having Plane Spanning Subgraph of Certain Type

Motivated by a result of [17], we determine necessary and sufficient conditions on $F\/$ with $|E(F)| \leq n-1\/$ for which $K_n - F\/$ admits a $g$-angulation. For $|E(F)| \geq n\/$, we investigate the possibility of placing $F\/$ in $K_n\/$ such that $K_n -F\/$ admits a $g$-angulation for certain families of graphs $F\/$.

math.CO↗
arXiv2017

Non-Crossing Perfect Matchings and Triangle-Free Geometric Graphs

We study extremal type problem arising from the question: What is the maximum number of edge-disjoint non-crossing perfect matchings on a set S of 2n points in the plane such that their union is a triangle-free geometric graph? We approach this problem by considering four different situations of S. In particular, in the general position, we obtain (i) a sufficient condition for the existence of n edge-disjoint non-crossing perfect matchings in the general position whose union is a maximal triangle-free geometric graph, and (ii) a lower bound on the number of edge-disjoint non-crossing perfect matchings whose union is a triangle free geometric graph.

math.CO↗
arXiv2017

On the maximum number of edges in plane graph with fixed exterior face degree

A well known Euler's formula consequence's corollary in graph theory states that: For a connected simple planar graph with $n$ vertices and $m$ edges, and girth $g$, we have $m \leq \frac{g}{g-2}(n-2)$. We show that a connected simple plane graph with $n$ vertices and girth $g$, and exterior face of degree $h$ has at most $\frac{g}{g-2}(n-2)- \frac{1}{g-2}(h-g)$ edges. A \emph{convex hull $g$-angulation} is a connected plane graph in which the exterior face is a simple $h$-cycle and all inner faces are $g$-cycles. For a given set $S$ of $n$ point in the plane having $h$ points in the boundary of its convex hull, we present the necessary and sufficient condition to obtain a convex hull $g$-angulation on $S$. We also determine the number of edges and inner faces in the convex hull $g$-angulation.

math.CO↗
arXiv2017

Fixed Point of A New Type Nonself Total Asymptotically Nonexpansive Mappings in Banach Spaces

In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for computing common fixed points of two nonself total asymptotically nonexpansive mappings are established in the framework of Banach spaces. Finally, we give an example which show that our theorems are applicable.

math.FA↗
arXiv2017

Generalized Convex Functions and Their Applications

This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex functions and establish some their properties. Moreover, we give generalized $ s $-convex functions in the second sense and present some new inequalities of generalized Hermite-Hadamard type for the class of functions whose second local fractional derivatives of order $ α$ in absolute value at certain powers are generalized $ s $-convex functions in the second sense. At the end, some examples that these inequalities are able to be applied to some special means are showed.

math.CA↗
arXiv2016

Triangulability of Convex Graphs and Convex Skewness

Motivated by a result of [1] which states that if F is a subgraph of a convex complete graph K_n and F contains no boundary edge of K_n and |E(F)| \leq n-3, then K_n - F admits a triangulation, we determine necessary and sufficient conditions on F with |E(F)| \leq n-1 for which the conclusion remains true. For |E(F)| \geq n, we investigate the possibility of packing F in K_n such that K_n -F admits a triangulation for certain families of graphs F. These results are then applied to determine the convex skewness of the convex graphs of the form K_n - F.

math.CO↗
arXiv2016

Boundedness of normalization generalized differential operator of fractional formal

Many authors have considered and investigated generalized fractional differential operators. The main object of this present paper is to define a new generalized fractional differential operator $\mathfrak{T}^{β,τ,γ},$ which generalized the Srivastava-Owa operators. Moreover, we investigate of the geometric properties such as univalency, starlikeness, convexity for their normalization. Further, boundedness and compactness in some well known spaces, such as Bloch space for last mention operator also are considered. Our tool is based on the generalized hypergeometric function.

math.FA↗
arXiv2016

On a fractional class of analytic function defined by using a new operator

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this operator, we introduce an interesting subclass of functions which are analytic and univalent. Furthermore, this effort covers coefficient bounds, distortions theorem, radii of starlikeness, convexity, bounded turning, extreme points and integral means inequalities of functions belongs to this class. Finally, applications involving certain fractional operators are illustrated.

math.CV↗
arXiv2016

Integral transforms defined by a new fractional class of analytic function in a complex Banach space

In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.

math.FA↗