Considering the importance of using nonlinear evolution equations in the investigation of many natural phenomena, in this paper, we consider the [Formula: see text]-dimensional Date–Jimbo–Kashiwara–Miwa ([Formula: see text]-dimensional DJKM) equation, we will investigate the solutions for this equation. Using the multiple exp functions method, we obtain analytical solutions for this equation, which are one-soliton, two-soliton and three-soliton solutions and these solutions include three categories of soliton wave solutions, i.e., one-wave solutions, two-wave solutions and three wave solutions. We have performed all calculations with a computer algebra system such as Maple and have also provided a graphical representation of the obtained solutions.
We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate a fractional Volterra integro-differential equation with the ψ-Hilfer fractional derivative in matrix-valued fuzzy k-normed spaces to obtain an approximation for this type of fractional equation.
In this paper, we consider a conformable fractional differential equation with a constant coefficient and obtain an approximation for this equation using the Radu–Mihet method, which is derived from the alternative fixed- point theorem. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers–Ulam-H-Fox stability for this equation. Finally, by providing numerical examples, we show the application of the obtained results.
In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order
σ
and introduce a class of control functions, i.e., Wright functions. Next, we apply the Cădariu-Radu method to prove the existence of a unique solution and Hyers-Ulam-Rassias-Wright stability of the fractional delay oscillation equation. At the end of the article, by an example, we show the application of the obtained results.
Our main goal in this paper is to investigate stochastic ternary antiderivatives (STAD). First, we will introduce the random ternary antiderivative operator. Then, by introducing the aggregation function using special functions such as the Mittag-Leffler function (MLF), the Wright function (WF), the H-Fox function (HFF), the Gauss hypergeometric function (GHF), and the exponential function (EXP-F), we will select the optimal control function by performing the necessary calculations. Next, by considering the symmetric matrix-valued FB-algebra (SMV-FB-A) and the symmetric matrix-valued FC-⋄-algebra (SMV-FC-⋄-A), we check the superstability of the desired operator. After stating each result, the superstability of the minimum is obtained by applying the optimal control function.
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