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Existence and stability of impulsive coupled system of fractional integrodifferential equations

100%

Zada A. , Waheed H. , Alzabut J. , Wang X.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

296--335

In this manuscript, we deal with a class and coupled system of implicit fractional differential equations, having some initial and impulsive conditions. Existence and uniqueness results are obtained by means of Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Hyers–Ulam stability is investigated by using classical technique of nonlinear functional analysis. Finally, we provide illustrative examples to support our obtained results.

Hyers-Ulam stability of a coupled system of fractional differential equations of Hilfer-Hadamard type

100%

Ahmad M. , Zada A. , Alzabut J.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

283--295

In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer-Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers-Ulam stability are also discussed. We provide an example demonstrating consistency to the theoretical findings.

An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem

100%

Amir F. , Farajzadeh A. , Alzabut J.

Journal of Applied Analysis

2022

tom Vol. 28, nr 2

333--340

Multiobjective optimization is the optimization with several conflicting objective functions. However, it is generally tough to find an optimal solution that satisfies all objectives from a mathematical frame of reference. The main objective of this article is to present an improved proximal method involving quasidistance for constrained multiobjective optimization problems under the locally Lipschitz condition of the cost function. An instigation to study the proximal method with quasi distances is due to its widespread applications of the quasi distances in computer theory. To study the convergence result, Fritz John’s necessary optimality condition for weak Pareto solution is used. The suitable conditions to guarantee that the cluster points of the generated sequences are Pareto-Clarke critical points are provided.

Further results on Ulam stability for a system of first-order nonsingular delay differential equations

100%

Zada A. , Pervaiz B. , Alzabut J. , Shah S. O.

Demonstratio Mathematica

2020

tom Vol. 53, nr 1

225--235

This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

On the nonoscillatory behavior of solutions of three classes of fractional difference equations

88%

Grace S. R. , Alzabut J. , Punitha S. , Muthulakshmi V. , Adiguzel H.

Opuscula Mathematica

2020

tom Vol. 40, no. 5

549--568

In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.