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In this paper, we apply the well-known aggregation mappings on Mittag-Leffler-type functions to investigating new approximation error estimates of a W-Hilfer fractional differential equation, by a different concept of Ulam-type stability in both bounded and unbounded domains.

This paper studies the uniqueness of the bounded solution to a new Cauchy problem of the fractional nonlinear partial integro-differential equation based on the multivariate Mittag–Leffler function as well as Banach’s contractive principle in a complete function space. Applying Babenko’s approach, we convert the fractional nonlinear equation with variable coefficients to an implicit integral equation, which is a powerful method of studying the uniqueness of solutions. Furthermore, we construct algorithms for finding analytic and approximate solutions using Adomian’s decomposition method and recurrence relation with the order convergence analysis. Finally, an illustrative example is presented to demonstrate constructions for the numerical solution using MATHEMATICA.

Stability is the most relevant property of dynamical systems. The stability of stochastic differential equations is a challenging and still open problem. In this article, using a fuzzy Mittag–Leffler function, we introduce a new fuzzy controller function to stabilize the stochastic differential equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting the fixed point technique, we are able to prove the fuzzy Mittag–Leffler–Hyers–Ulam–Rassias stability of the SDE.

We apply special functions and use the concept of the aggregation function to introduce a new class of fuzzy control functions, and based on this, we obtain the best approximation for the stochastic bi-homomorphisms and stochastic bi-derivations in FB-algebras and FC-⋄-algebras of matrix type associated with the bi-additive random operator inequality.

By using a class of aggregation control functions, we introduce the concept of multiple-HU-OS1-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We apply an alternative fixed-point theorem to prove the existence of a unique solution and the multiple-HU-OS1-stability for the NS-ABC-FDE in the symmetric matrix-valued FBS. Finally, with 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.

This paper introduces a complete Gn-Menger space and defines the Hausdorff–Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-θ-contractions in fractal spaces.

In this work, by considering a class of matrix valued fuzzy controllers and using a (κ,ς)-Cauchy–Jensen additive functional equation ((κ,ς)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, and obtain the existence of a unique solution and the H–U–R stability (Hyers–Ulam–Rassias) for the homomorphisms and Jordan homomorphisms on Lie matrix valued fuzzy algebras with ς members (ς-LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained.

We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an approximation for a pseudo functional equation is called random HUR stability. We use a fixed point technique derived from the alternative fixed point theorem (FPT) to investigate random HUR stability of the Riemann–Liouville fractional equations in MB-spaces. As an application, we introduce a class of random Wright control function and investigate existence–uniqueness and Wright stability of these equations in MB-spaces.

In this article, we introduce the ∗-fuzzy (L+)p spaces for 1≤p

Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii&rsquo, s fixed-point theorem in a cone, as well as some inequalities relevant to Green&rsquo, s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative [...]