Manzoor Ahmad

In this study, we investigate an analytical technique for solving the newly developed time-fractional [ ]-dimensional Jimbo–Miwa [ ] equation in the framework of the conformable fractional derivative. The exact solutions are constructed using the Generalized-Kudryashov-Auxiliary-Jacobian method (GKAJM), which is flexible, efficient, and does not require additional mathematical manipulations. To the best of our knowledge, this method has not previously been employed to obtain exact solutions of the time-fractional [ ]-dimensional [ ] equation. The proposed approach yields a wide class of exact solutions expressed in logarithmic, exponential, trigonometric, and hyperbolic forms. By choosing appropriate parameter values, the obtained solutions exhibit significantly different dynamical behaviors, including kink-type solitary wave solutions, bell-shaped solitary wave solutions, bright soliton solutions, dark solitary wave solutions, kink-type singular waves, a train of singular solitons, static blow-up-type wave solutions, and rogue-wave-like localized structure solutions. Furthermore, the effectiveness of the method demonstrates its applicability to other nonlinear evolution equations and contributes to a deeper understanding of wave propagation phenomena in water wave dynamics. The results comprehensively describe the perturbed wave dynamics associated with the time-fractional [ ]-dimensional [ ] equation.

This article is concerned with the existence and uniqueness of solutions of a nonlinear neutral conformable fractional differential system with infinite delay, involving conformable fractional derivative. Additionally, we study the Ulam--Hyres stability, Ulam--Hyres--Mittag--Leffler stability, Ulam--Hyres--Mittag--Leffler--Rassias stability for the solutions of considered system using Picard operator. For application of the theory, we add an example at the end.

The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result.

This paper is devoted to the study of stochastic fractional differential equations. Particularly, we study the existence and uniqueness of solutions of nonlinear stochastic weighted impulsive ψ -Hilfer neutral integro-fractional differential system with infinite delay. We obtain the results with the help of fixed-point theorems and Banach contraction principle. Additionally, we investigate the Ulam–Hyers stability of the solutions using basic schemes of fractional calculus. For application of the theory, we add an example.

This work is committed to establish the necessary assumptions related with the existence and uniqueness of solutions to a nonlocal coupled impulsive fractional differential equation. We attain our main results by the use of Krasnoselskïï’s fixed point theorem and Banach contraction principle. Additionally, we create a framework for studying the Hyers–Ulam stability of the considered problem. For the applications of theoretical result, we discuss an example at the end.

This article concerns with the existence and uniqueness for a new model of implicit coupled system of neutral fractional differential equations involving Caputo fractional derivatives with respect to the Chebyshev norm. In addition, we prove the Hyers–Ulam–Mittag-Leffler stability for the considered system through the Picard operator. For application of the theory, we add an example at the end. The obtained results can be extended for the Bielecki norm.

In this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results.

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.