mohammad esmael samei

‎The pantograph equation improves the mathematical model of the system includes modeling the motion of the wire connected with the dynamics of the supports and modeling the dynamics of the pantograph‎. ‎The subject of this paper is the existence and Ulam stability of solutions for a coupled system of sequential pantograph equations of fractional order involving both Riemann-Liouville and Caputo-Hadamard fractional derivative operators‎. ‎By applying the classical theorems in nonlinear analysis‎, ‎such as the Banach's fixed point theorem and Leray-Schauder nonlinear alternative‎, ‎the uniqueness and existence of solutions are obtained‎. ‎Furthermore‎, ‎the Ulam stability results are also presented‎. ‎Finally‎, ‎we have shown the results in the applications section by presenting various examples to numerical effects which provided to support the theoretical findings.

In this paper, we intend to investigate the solutions of the fractional differential inclusion system with successive derivatives with the Laplace operator and according to the derivative and integral boundary conditions. In this regard, we use the fixed point and end point theorems. Finally, we will show this device's effectiveness by providing some practical examples.

In this paper, we introduce an extension of the Hilfer fractional derivative, the "Hilfer fractional quantum derivative", and establish some of its properties. Then, we introduce and discuss initial and boundary value problems involving the Hilfer fractional quantum derivative. The existence of a unique solution of the considered problems is established via Banach's contraction mapping principle. Examples illustrating the obtained results are also presented.

This paper deals with the stability results for the solution of a fractional $q$--integro-differential problem with integral conditions. Using Krasnoselskii's, and Banach's fixed point theorems, we prove the existence and uniqueness of results. Based on the results obtained, conditions are provided that ensure the generalized Ulam stability of the original system on a time scale. The results are illustrated by the examples under the numerical technique.

This paper tries to show that there is only one solution for problem of fractional $q$-differential equations with  Hilfer type, and it does so by using a particular method known as Schaefer's fixed point theorem  and the Banach contraction principle. After that, we create a integral  type of the  problem for nonlocal condition. Next, we show that Ulam stability is true. The Gr"{o}wnwall rule for singular kernels of the equations helps to show our findings are correct. We confirm our findings by giving a few practical examples.

The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order .The q-fractional differential equation usually describes the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative 𝐷 𝑐 𝑞 𝛼𝑥(𝑡), of Caputo type with order 0 < 𝛼 < 1 and scale index 0 < 𝑞 < 1. We establish a rigorous truncation error boundness and prove that this difference formula is unconditionally stable. Then, we consider the difference method for solving the initial problem of q-fractional differential equation: 𝐷𝑞 𝛼𝑥(𝑡) = 𝑓(𝑡, 𝑥(𝑡)) 𝑐 . We prove the existence and stability of the difference solution and give the convergence analysis. Numerical experiments show the effectiveness and high accuracy of the proposed difference method.

In this scheme, we first present a difference formula (called the 𝐿1,𝑞 formula) to discretize the fractional q-derivative 𝐷 𝑐 𝑞 𝛼𝑥(𝑡), of Caputo type with 0 < 𝛼, 𝑞 < 1. This difference formula is constructed by using the piecewise linear interpolation to approximate the integral function. Then, by using this difference formula, we establish a difference method for solving the initial problem of q-fractional differential equation.

We prove that this difference method is unconditionally stable and give an error estimation of ∆𝑡𝑛 2 -order. Numerical experiments show the high accuracy and effectiveness of this difference formula. To the authors’ best knowledge, it is the first time that an unconditionally stable difference formula is presented and analyzed for the q-fractional problems. Our work provides a numerical approach for solving the q-fractional problems.

The following conclusions were drawn from this research.  We present the difference formula and drive truncation error boundness.  The formula is contributed to the stability analysis.  The difference technique is used to solve the initial value problem of q-fractional differential equation.  The existence of the solution, stability and error estimation are given for the difference formula.

IIn this paper, we prove the Mittag-Leffler-Hyers-Ulam-Rassias stability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions.

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive result on the Nadler contraction theorem for multivalued mappings in this space. In the following, by expressing pseudo-Banach-type pairs of mappings, we study the conditions for the existence of a unique coupled strong fixed point in these mappings. Pseudo-Chatterjae mapping $F:X times Xto X$ satisfies in [dleft( F(x, y), F(u, v) right) leq k max left{ dleft( x, F(u, v)right), dleft( F(x, y), uright) right}, ] where $x, v in A$, $y, u in B$ and $0 < k < frac{1}{2}$. Also, We define some quasi-Banach and Pseudo-Chatterjae contraction inequalities. In addition, we will prove theorems about coupled fixed points. Finally, several examples are presented to understand the our results.

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach contraction principle is that it also gives the convergence of an iterative scheme to a unique fixed point. In this paper,  we consider (X, M, *) to be fuzzy metric spaces in Park's sense and we show our results for fixed points of contractive and nonexpansive multifunctions on Hausdorff fuzzy metric space.

In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory and graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, we present some iterative scheme results for G -fuzzy contractive and G -fuzzy nonexpansive mappings on graphs.