NOVEL METHODS FOR SOLVING THE CONFORMABLE WAVE EQUATION

In this paper, a two-dimensional conformable fractional wave equation describing a circular membrane undergoing axisymmetric vibrations is formulated. It was found that the analytical solutions of the fractional wave equation using the conformable fractional formulation can be easily and efficiently obtained using separation of variables and double Laplace transform methods. These solutions are compared with the approximate solution obtained using the differential transform method for certain cases

The bounds for the distance two labelling and radio labelling of nanostar tree dendrimer

The distance two labelling and radio labelling problems are applicable to find the optimal frequency assignments on AM and FM radio stations. The distance two labelling, known as L(2,1)-labelling of a graph A, can be defined as a function, , from the vertex set V(A) to the set of all nonnegative integers such that (, ) represents the distance between the vertices c and s in where the absolute values of the difference between () and () are greater than or equal to both 2 and 1 if (, )=1 and (, ) = 2, respectively. The L(2,1)-labelling number of , denoted by 2,1 (), can be defined as the smallest number j such that there is an (2,1) −labeling with maximum label j. A radio labelling of a connected graph A is an injection k from the vertices of to such that (, ) + |() − ()| ≥ 1 + ∀ , ∈ (), where represents the diameter of graph . The radio numbers of and A are represented by () and () which are the maximum number assigned to any vertex of and the minimum value of () taken over all labellings k of , respectively. Our main goal is to obtain the bounds for the distance two labelling and radio labelling of nanostar tree dendrimers

Economic Models Involving Time Fractal

In this article, the price adjustment equation has been proposed and studied in the frame of fractal calculus which plays an important role in market equilibrium. Fractal time has been recently suggested by researchers in physics due to the self-similar properties and fractional dimension. We investigate the economic models from the viewpoint of local and non-local fractal Caputo derivatives. We derive some novel analytical solutions via the fractal Laplace transform. In fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard computational sense, and the non-local fractal Caputo fractal derivative is a generalization of the non-local fractional Caputo derivative. The economic models involving fractal time provide a new framework that depends on the dimension of fractal time. The suggested fractal models are considered as a generalization of standard models that present new models to economists for fitting the economic data. In addition, we carry out a comparative analysis to understand the advantages of the fractal calculus operator on the basis of the additional fractal dimension of time parameter, denoted by $alpha$, which is related to the local derivative, and we also indicate that when this dimension is equal to $1$, we obtain the same results in the standard fractional calculus as well as when $alpha$ and the nonlocal memory effect parameter, denoted by $gamma$, of the nonlocal fractal derivative are both equal to $1$, we obtain the same results in the standard calculus

Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable formula of finite increments

On Conformable Laplace’s Equation

The most important properties of the conformable derivative and integral have been recently introduced. In this paper, we propose and prove some new results on conformable Laplace’s equation. We discuss the solution of this mathematical problem with Dirichlet-type and Neumann-type conditions. All our obtained results will be applied to some interesting examples

Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations

Abstract We study sequential fractional pantograph q-differential equations. We establish the uniqueness of solutions via Banach’s contraction mapping principle. Further, we define and study the Ulam–Hyers stability and Ulam–Hyers–Rassias stability of solutions. We also discuss an illustrative example