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Items from 1 to 20 out of 38 results

article

Existence, uniqueness, and Ulam stability of solutions of fractional conformable Langevin system on the ethane graph

Guotao Wang, Hualei Yuan

Mathematical Methods in the Applied Sciences > 47 > 9 > 7350 - 7371

The present study examines the Langevin coupled boundary value problem with the fractional conformable derivative on the ethane graph. The main objective of this research is to establish the existence and uniqueness of solutions with the help of the fixed point theorem and to analyze the Ulam stability of the corresponding problem. Several examples are provided to demonstrate the obtained results.

article

Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative

Ho Vu, John M. Rassias, Ngo Van Hoa

Mathematical Methods in the Applied Sciences > 46 > 1 > 438 - 460

The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP‐FDEs) via the concept of Caputo fractional derivative with respect to another function with the order

α \in (1,2)

. The existence and uniqueness results of a solution for BVP‐FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide...

article

On implicit fractional q‐difference equations: Analysis and stability

Nadjet Laledj, Abdelkrim Salim, Jamal Eddine Lazreg, Saïd Abbas, more

Mathematical Methods in the Applied Sciences > 45 > 17 > 10775 - 10797

This paper deals with some existence and Ulam stability results for some classes of implicit fractional

q

‐difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point...

article

Stabilities and instabilities of an advanced quartic functional equation in various normed spaces

Beri V. Senthil Kumar, Hemen Dutta, Sriramulu Sabarinathan

Mathematical Methods in the Applied Sciences > 44 > 14 > 11469 - 11481

In this paper, a new and advanced quartic functional equation is introduced, and its classical stability results in various normed spaces are discussed. An appropriate illustration is also presented to invalidate the stability result for a very critical instance. At the end of this paper, we have concluded that the stability results are valid in various normed spaces.

article

Existence and Ulam's type stability results for a class of fractional boundary value problems on a star graph

Wei Zhang, Wenbin Liu

Mathematical Methods in the Applied Sciences > 43 > 15 > 8568 - 8594

This paper is concerned with a nonlinear fractional boundary value problem on a star graph. By using a transformation, the suggested problem is converted into an equivalent system of fractional boundary value problem. Schaefer's fixed point theorem and Banach's contraction principle is used to establish its existence and uniqueness results. Further, different kinds of Ulam's type stability results...

article

Ulam‐type stability for differential equations driven by measures

Bianca‐Renata Satco

Mathematische Nachrichten > 293 > 1 > 147 - 157

Based on a notion of Stieltjes derivative of a function with respect to another function, we provide Ulam–Hyers type stability results for nonlinear differential equations driven by measures on compact or on unbounded intervals, in the lack of Lipschitz continuity assumptions. In particular, one can deduce stability results for generalized differential equations, dynamic equations on time scales or...

article

On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative

Tamer Nabil

Journal of Mathematics and Applications > 2020 > Vol. 43 > 99--112

In this article, the solvability of fractional neutral differential equation involving ψ-Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.

article

Stability analysis of a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem

JinRong Wang, Akbar Zada, Hira Waheed

Mathematical Methods in the Applied Sciences > 42 > 18 > 6706 - 6732

In this article, we study the existence and uniqueness of solution for a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem. Further, we investigate different kinds of stability such as Ulam‐Hyers stability, generalized Ulam‐Hyers stability, Ulam‐Hyers‐Rassias stability, and generalized Ulam‐Hyers‐Rassias stability. We develop conditions for existence and uniqueness...

article

Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations

Sajjad Ali, Thabet Abdeljawad, Kamal Shah, Fahd Jarad, more

Advances in Difference Equations > 2019 > 2019 > 1 > 1-19

In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative...

article

On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations

Sajjad Ali, Kamal Shah, Fahd Jarad

Mathematical Methods in the Applied Sciences > 42 > 3 > 969 - 981

In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone iterative technique together with upper and lower solutions, conditions for the existence and approximation of minimal and maximal solutions to the BVP under consideration are constructed...

article

On the Existence and Stability of Boundary Value Problem for Differential Equation with Hilfer-Katugampola Fractional Derivative

E. M. Elsayed, S. Harikrishnan, K. Kanagarajan

Acta Mathematica Scientia > 2019 > 39 > 6 > 1568-1578

In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer’s fixed point theorem, Banach contraction principle and Ulam type stability.

article

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Mouffak Benchohra, Soufyane Bouriah, Juan J. Nieto

Demonstratio Mathematica > 2019 > Vol. 52, nr 1 > 437--450

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability...

article

Ulam stability to a toppled systems of nonlinear implicit fractional order boundary value problem

Zeeshan Ali, Akbar Zada, Kamal Shah

Boundary Value Problems > 2018 > 2018 > 1 > 1-16

In this manuscript, we give some sufficient conditions for existence, uniqueness and various kinds of Ulam stability for a toppled system of fractional order boundary value problems involving the Riemann–Liouville fractional derivative. Applying the Banach contraction principle and the Leray–Schauder result of cone type, uniqueness and existence results are proved for the proposed toppled system....

article

The z-transform method for the Ulam stability of linear difference equations with constant coefficients

Yonghong Shen, Yongjin Li

Advances in Difference Equations > 2018 > 2018 > 1 > 1-15

Applying the z-transform method, we study the Ulam stability of linear difference equations with constant coefficients. To a certain extent, our results can be viewed as an important complement to the existing methods and results.

article

Fixed-point theorem in classes of function with values in a dq-metric space

Janusz Brzdęk, El-sayed El-hady, Zbigniew Leśniak

Journal of Fixed Point Theory and Applications > 2018 > 20 > 4 > 1-16

We prove a fixed point result for nonlinear operators, acting on some classes of functions with values in a dq-metric space, and show some applications of it. The result has been motivated by some issues arising in Ulam stability. We use a restricted form of a contraction condition.

article

A General Method for the Ulam Stability of Linear Differential Equations

Yonghong Shen, Yongjin Li

Bulletin of the Malaysian Mathematical Sciences Society > 2019 > 42 > 6 > 3187-3211

This paper deals with the Ulam stability of linear differential equations by using the method of variation of parameters, which provides a unified method to study the Ulam stability problem of linear differential equations of n-th order with constant and nonconstant coefficients. As an application of the main results, we also obtain the Hyers–Ulam stability of the Cauchy–Euler differential equations...

article

On fixed points of a linear operator of polynomial form of order 3

Janusz Brzdȩk, El-sayed El-hady, Zbigniew Leśniak

Journal of Fixed Point Theory and Applications > 2018 > 20 > 2 > 1-10

Let X be a complex linear space, endowed with an extended (that is, admitting infinite values) norm. We prove a fixed point theorem for operators of the form $$p_3 \mathcal {L}^3 + p_2 \mathcal {L}^2 +p_1\mathcal {L}$$ p3L3+p2L2+p1L , where $$ \mathcal {L}:X\rightarrow X$$ L:X→X is linear and $$p_1,p_2,p_3$$ p1,p2,p3 are fixed scalars. That result has been motivated by some issues arising in Ulam...

article

On Ulam’s Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations

Zeeshan Ali, Akbar Zada, Kamal Shah

Bulletin of the Malaysian Mathematical Sciences Society > 2019 > 42 > 5 > 2681-2699

In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractional differential equations involving Caputo derivative. We develop conditions for uniqueness and existence...

article

Approximate homomorphisms on lattices

Roman Badora, Tomasz Kochanek, Barbara Przebieracz

Archiv der Mathematik > 2018 > 111 > 2 > 177-186

We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain systems of lattice neighborhoods. As a corollary, we obtain a stability result for approximately monotone functions.

article

Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions

D. Vivek, K. Kanagarajan, E. M. Elsayed

Mediterranean Journal of Mathematics > 2018 > 15 > 1 > 1-21

The aim of this paper is to establish the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer’s fixed point theorem and Banach contraction principle. Next, we establish the equivalent mixed-type integral for nonlocal condition. Further we prove the Ulam stability results. The Gronwall’s lemma for singular kernels plays an important role...

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Search results

Existence, uniqueness, and Ulam stability of solutions of fractional conformable Langevin system on the ethane graph

Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative

On implicit fractional q‐difference equations: Analysis and stability

Stabilities and instabilities of an advanced quartic functional equation in various normed spaces

Existence and Ulam's type stability results for a class of fractional boundary value problems on a star graph

Ulam‐type stability for differential equations driven by measures

On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative

Stability analysis of a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem

Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations

On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations

On the Existence and Stability of Boundary Value Problem for Differential Equation with Hilfer-Katugampola Fractional Derivative

Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Ulam stability to a toppled systems of nonlinear implicit fractional order boundary value problem

The z-transform method for the Ulam stability of linear difference equations with constant coefficients

Fixed-point theorem in classes of function with values in a dq-metric space

A General Method for the Ulam Stability of Linear Differential Equations

On fixed points of a linear operator of polynomial form of order 3

On Ulam’s Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations

Approximate homomorphisms on lattices

Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions

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