This paper studies the (3 + 1) extended Zakharov–Kuznetsov (EZK) dynamical equation that is utilized to describe nonlinear three-dimensional dust-ion-acoustic solitary waves in a magnetized two-ion-temperature dusty plasma. The bifurcation theory for planar dynamical systems is applied to the EZK equation. For a given restriction on the parameters, some new traveling wave solutions are characterized in terms of Jacobi-elliptic functions. These solutions are clarified in a graphical way. Physically, these wave solutions represent the related electric potential. Based on Maxwell equations, we calculate the corresponding electric magnetic fields, and we clarify them graphically.

In this article, we study the existence of a solution to the mixed hybrid fractional differential equations of sequential type with nonlocal integral hybrid boundary conditions. The main results are established with the aid of Darbo’s fixed point theorem and Hausdorff’s measure of noncompactness method. The stability of the proposed fractional differential equation is also investigated using the Ulam–Hyer technique. In addition, an applied example that supports the theoretical results reached through this study is included.

This article presents a study of the existence and uniqueness of solutions for a system of hybrid fractional differential equations involving fractional derivatives of the Caputo-Hadamard type with three-point hybrid boundary conditions. In addition to this, the “Hyres–Ulam” stability of the solutions for this type of equation is verified, and finally a numerical example was presented to support our theoretical results.

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