## About

234

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Introduction

Fuzzy sets, Intuitionistic fuzzy sets theory and its applications in partial differential equations.
Generalised functions theory (Colombeau algèbra).
dynamical systems

Additional affiliations

September 2008 - present

## Publications

Publications (234)

In this paper, we study the existence result of solutions for fuzzy nonlinear fractional differential equations involving Caputo differentiability of an arbitrary order 0 < q < 1. As application, an example is included to show the applicability of our result.

In this paper, we establish a new result concerning the existence and uniqueness of solutions for nonlinear fractional differential equations with fuzzy boundary conditions. As application, we give an illustrative example to show the effectiveness of the obtained result.

n this paper, we study the existence and uniqueness of an intuitionistic fuzzy solution for semi-linear intuitionistic fuzzy integro-differential equations with non-local conditions using the Banach fixed point theorem. Theorem on the existence and uniqueness of intuitionistic fuzzy solution for these problems with nonlocal conditions are presented...

Our purpose is to establish the existence of weak solutions to Neumann boundary value problem for equations involving the p(x)-Laplacian-like operator and the p(x)-Laplacian operator. The existence proof is based on the theory of the variable exponent Sobolev spaces and the topological degree theory. Our result extend and generalize several corresp...

The notion of inclusion by generalized conformable differentiability is used to
analyze fuzzy conformable differential equations (FCDE). This idea is based on
expanding the class of conformable differentiable fuzzy mappings, and we use generalized lateral conformable derivatives to do so. We’ll see that both conformable
derivatives are distinct and...

The main crux of this manuscript is to develop the theory of fractional hybrid differential equations with linear perturbations of second type involving ψ−Caputo fractional derivative of an arbitrary order α ∈ (0, 1). By applying Krasnoselskii fixed point theorem and some basic concepts on fractional analysis, we prove the existence of solutions fo...

In this paper we proved some importance proprieties of Colombeau algebra, we proved the existence and uniqueness of solution of transport equation with variable speed and initial data in the Colombeau algebra G. We proved the association of the generalized solution with the classical solution.

This article is related to present and solve the theory of fractional hybrid differential equations with fuzzy initial values involving the fuzzy Riemann-Liouville fractional differential operators of order $0 < q < 1$. For the concerned presentation, we study the existence and uniqueness of a fuzzy solution are brought in detail basing on the conc...

In the present article, we investigate a new concept of fixedpoint theorems in the framework of Colombeau algebra of gen-eralized funtions. introduce a characterisation of the continuity of some C−linear maps, We gave another representation of the contraction of the maps among Colombian algebras.In addition, wehave given a general frame of fixed-po...

In this paper, we establish the global well-posedness and analyticity of the 3D fractional magnetohydrodynamics equations in the critical Fourier-Besov-Morrey spaces with variable exponent, which can be seen as a meaningful complement to the corresponding results of the magnetohydrodynamics equations in usual Fourier-Besov-Morrey spaces. Furthermor...

This paper proves the existence and uniqueness of solution of irregular transport problem with variable speed and initial data in the Colombeau algebra G, and some important proprieties of Colombeau algebra. The existence of distribution solutions to some classes of such equations is proven.

This paper is concerned with the existence of "weak solution" for a Dirichlet boundary value problems involving the p(x)-Laplacian operator depending on three real parameters. The proof of the main result is constructed by utilizing the topological degree for a class of demicontinuous operators of generalized (S+) type and the theory of variable-ex...

In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving the p ( x ) p(x) -Laplacian-like operator. Using a topological degree theory for a class of demicontinuous operators of generalized ( S + ) (S_{+}) -type and the theory of the variable exponent Sobolev spaces, we establi...

In this work, the authors consider the initial value problems in intuitionistic fuzzy ordinary differential equations. The one-step method for approximating the solution of these problems has been defined. The convergence, consistency, and stability of the difference method for approximating the solution of intuitionistic fuzzy differential equatio...

In this article, we consider a Neumann boundary value problem driven by p ( x )-Laplacian-like operator with a reaction term depending also on the gradient (convection) and on three real parameters, originated from a capillary phenomena, of the following form: − Δ p ( x ) l u + δ | u | ζ ( x ) − 2 u = μ g ( x , u ) + λ f ( x , u , ∇ u ) in Ω , ∂ u...

In this paper, we introduce a new class of control functions, namely extended FZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{FZ}$\end{document}-simulation fu...

We establish an existence and uniqueness results for a homogeneous Neumann boundary value problem involving the p(x)-Kirchhoff-Laplace operator of the following form -M(∫Ω1p(x)(|∇u|p(x)+|u|p(x))dx)(div(|∇u|p(x)-2∇u)-|u|p(x)-2u)=f(x,u,∇u)in,|∇u|p(x)-2∂u∂η=0on∂Ω.where Ω is a smooth bounded domain in RN, ∂u∂η is the exterior normal derivative, p(x)∈C+...

We provide a fractional-order fuzzy fractional differential equation q ∈ (0, 1]. A fuzzy fractional integral and a fuzzy conformable derivative are shown and proved. To prove fuzzy solutions for fractional differential equations with fuzzy beginning values and deterministic or fuzzy functions, two alternative techniques are used. The application ha...

The removal of a ternary mixture of cationic dyes, Basic Blue 41 (BB41), Safranin (SAF), and Basic Yellow 28 (BY28) onto Bombax buonopozense bark as a new eco-friendly adsorbent was studied experimentally and theoretically in single as in ternary system, to explore the removal efficiency of the complex mixture and the increase in the number of spec...

This paper deals with the study of a coupled system of generalized impulsive integro-differential evolution equations with periodic boundary value. We show the existence and uniqueness of the solution for the proposed problem using Banach fixed point theorem. Another way was used to show the existence result with the aim of breaking out of the wide...

This research establishes the existence of weak solution for a Dirichlet boundary value problem involving the p ( x )-Laplacian-like operator depending on three real parameters, originated from a capillary phenomena, of the following form: $$\begin{aligned} \displaystyle \left\{ \begin{array}{ll} \displaystyle -\Delta ^{l}_{p(x)}u+\delta \vert u\ve...

In this paper, we study some criteria for three types of convergence of series of fuzzy numbers, using the usual order relation ex�tended to intervals and fuzzy numbers. Then, we prove a fuzzy version of Abel theorem for fuzzy series, we introduce the fuzzy Cauchy product of two fuzzy series, which we apply to prove the main properties of the
expon...

In the present paper, we first introduce a new intuitionistic fuzzy distance. Relationships between three kinds of convergences compared to this distance are studied in this paper. We will give necessary and sufficient conditions to have a convergence equivalence for these four metrics.

This paper is devoted to the existence and uniqueness result to the following problem: 1d2dt2u(t,x)+Au(t,x)=F(t,u(t,x))x∈R,t≥0u(0,x)=a0(x),∂tu(0,x)=b0(x)a0 and b0 are singular generalized functions and F satisfies L∞ logarithmic type, A is an operator defined from the Colombeau’s algebra in itself. Nets of cosine family (Cε)ε with polynomial growth...

The paper studies the existence of a weak solutions for Neumann problems with p(x)-Laplacian-like operators, originated from a capillary phenomena, of the following form -div|∇u|p(x)-2∇u+|∇u|2p(x)-2∇u1+|∇u|2p(x)=μ|u|α(x)-2u+λf(x,u,∇u)inΩ,|∇u|p(x)-2∇u+|∇u|2p(x)-2∇u1+|∇u|2p(x)∂u∂η=0on∂Ω,in the setting of the generalized Sobolev spaces W1,p(x)(Ω), whe...

In this manuscript, we are concerned with the existence result of nonlinear hybrid differential equations involving ψ−Caputo fractional derivatives of an arbitrary order α ∈ (0, 1). By applying Krasnoselskii fixed point theorem and some fractional analysis techniques, we prove our main result. As application, a nontrivial example is given to demons...

In this paper, we investigate the boundary value problems for nonlinear ψ−Caputo fractional differential equations involving the p−Laplacian operator. We establish a new result on the existence and uniqueness of solutions by employing Banach fixed point theorem. As application, several examples are presented to illustrate the proposed result.

This manuscript is devoted to the investigation of the existence results of fractional Cauchy problem for some nonlinear ψ−Caputo fractional dierential equations with non local conditions. By applying fixed point theorems, some results of topological degree theory for condensing maps and some fractional analysis techniques, we establish some new ex...

In this paper, we introduce two new concepts, generalized α-η-FZ-contraction and modified α-η-FZ-contraction, which unify several types of contractions in the context of fuzzy metric spaces. We discuss the existence and uniqueness results of such mappings in the setting of a complete fuzzy metric space in the sense of George and Veeramani and prese...

The aim of this paper first presents a new solution to the SIR model with fuzzy initial value, elementary properties of this new solution are given. We study the application of variational iteration method in finding the approximate solution of SIR model with fuzzy initial value. The presented method have been applied in a direct way without linear...

In this paper, we use an intuitionistic fuzzy Laplace transforms for solving intuitionistic fuzzy hyperbolic equations precisely the transport equation with intuitionistic fuzzy data under strongly generalized H-differentiability concept. For this purpose, the intuitionistic fuzzy transport equation is converted to the intuitionistic fuzzy boundary...

In this paper, we investigate the existence of a "weak solutions" for a Neumann problems of $p(x)$-Laplacian-like operators, originated from a capillary phenomena, of the following form \begin{equation*} \displaystyle\left\{\begin{array}{ll} \displaystyle-{\rm{div}}\Big(\vert\nabla u\vert^{p(x)-2}\nabla u+\frac{\vert\nabla u\vert^{2p(x)-2}\nabla u}...

In this paper, we develop a new numerical algorithm for solving a time dependent convection-diffusion equation with Dirichlet’s type boundary conditions. The method comprises the horizontal method of lines for time integration and ( θ -method, θ ∈ [1/2, 1] ( θ = 1 corresponds to the backward Euler method and θ = 1/2 corresponds to the Crank-Nicolso...

This paper establishes the existence and uniqueness, and also presents a blow-up criterion, for solutions of the quasi-geostrophic (QG) equation in a framework of Fourier type, specifically Fourier-Besov-Morey spaces. If it is assumed that the initial data \(\theta _0\) is small and belonging to the critical Fourier-Besov-Morrey spaces \(\mathscr {...

In the present paper, we use the generalized differentiability concept to study the intuitionistic fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with intuitionistic fuzzy initial condition. To illustrate the results, we will solve an advection equation using the finite difference method.

In this paper we investigate the existence result of solutions for boundary value problem of nonlinear fuzzy fractional differential equations involving Caputo fuzzy fractional derivatives. We conclude our work by presenting an illustrative example.

In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.
1. Introduc...

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this manuscript, we establish new existence and uniqueness results for fuzzy linear and semilinear fractional evolution equations in...

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

The purpose of this paper is to investigate the existence and uniqueness of intuitionistic fuzzy solutions for integral boundary value problems for intuitionistic fuzzy delay partial differential equations with integral boundary initial conditions in a complete metric space using the Banach fixed point theorem, as well as computational examples to...

In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.
1. Introduction...

In this paper, we used new conformable variational iteration method, by the conformable derivative, for solving fractional heat-like and wave-like equations. This method is simple and very effective in the solution procedures of the fractional partial differential equations that have complicated solutions with classical fractional derivative defini...

In this work, the purpose is to discuss the homotopy analysis method (HAM) for the use of intuitionistic fuzzy differential equations with the linear differential operator. Furthermore, a numerical example is presented to shed light on the capability of the present method, and the numerical results illustrated by adopting the homotopy perturbation...

This paper addresses the issue of the existence and uniqueness of intuitionistic fuzzy solutions for some classes of partial functional differential equations with state-dependent delay in a new weighted complete metric space. Theorems on the existence and uniqueness of intuitionistic fuzzy solutions for these problems with integral boundary condit...

In this study, we introduce new concepts of -contraction and -contraction and we discuss existence results of the best proximity points of such types of non-self-mappings involving control functions in the structure of complete fuzzy metric spaces. Our results extend, generalize, enrich, and improve diverse existing results in the current literatur...

Results reported in this article prove the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations supplemented by nonseparated boundary value conditions. We consider a new norm to establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained...

In this paper, we study the existence and uniqueness results of solution for the intuitionistic fuzzy nonlinear fractional differential equations involving the Caputo concepts of fractional derivative. In addition, we establish essentially the Mittag-Leffler stability result for the intuitionistic fuzzy nonlinear fractional differential equations b...

In the present paper, we study generalized conformable differentiability
concepts for fuzzy valued functions. Existence of the solutions of fuzzy fractional
differential equations involving generalized conformable differentiability is studied. Also, some concrete applications to ordinary fuzzy fractional differential equations
with fuzzy initial va...

In the present paper, we study generalized conformable differentiability concepts for fuzzy valued functions. Existence of the solutions of fuzzy fractional differential equations involving generalized conformable differentiability is studied. Also, some concrete applications to ordinary fuzzy fractional differential equations with fuzzy initial va...

In this paper, the generalized concept of conformable fractional derivatives of order for fuzzy functions is introduced. We presented the definition and proved properties and theorems of these derivatives. The fuzzy conformable fractional differential equations and the properties of the fuzzy solution are investigated, developed, and proved. Some e...

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give...

In this paper, we discuss the existence and uniqueness of boundary value problems for sequential ψ-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions. The existence results are obtained via the well known Krasnoselskii's fixed point theorem while the uniqueness is demonstrated by using the Banach's contracti...

In this paper, we investigate the existence and uniqueness of a coupled system of nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. We use Banach’s and Krasnoselskii’s fixed point theorems to obtain the results. Lastly, we give two examples to show the effectiveness of the main results.
1. Introduction
In...

This paper discusses a boundary value problem of nonlinear fractional integrodifferential equations of order and and boundary conditions of the form . Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem...

This paper deals with the outbreak of COVID-19 in Brazil. The new focus of the Corona epidemic via an introduced mathematical model, and a relationship between the stability of COVID-19 free and pandemic equilibrium points and the basic reproduction rate has been studied. According to the presented model, we give pandemic prediction for a short per...

Recently, a new fuzzy fractional derivative called the fuzzy generalized conformable fractional derivative is given which is based on the basic limit definition of the derivative in Harir et al. (Adv Fuzzy Syst Article ID 1954975, 7 (2019), https://doi.org/10.1155/2020/1954975). In this paper, we study a fuzzy conformable Laplace transform and unde...

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differ...

The objective of this paper is to investigate the existence and uniqueness for a nonlinear fractional integro-differential equations with integral and anti-periodic boundary conditions by means of fixed point theorems. The existence of solutions is obtained from the well known Krasnoselskii’s fixed point theorem, whereas the uniqueness of solutions...

This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes...

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that ha...

This book provides an overview of the state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. Covering topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods...

In this paper,we propose amethod for solving intuitionistic fuzzy systems
of linear equations. The method is discussed in detail and considered in two cases,
namelywith the right hand side as an intuitionistic fuzzy vector and as an intuitionistic
fuzzy symmetric vector. Finally,we solve numerical examples in order to demonstrate
the applicability...

In this work, we generalize the definition of a fuzzy strongly continuous semigroup and it’s generator. We establish some of their proprieties and some results about the existence and uniqueness of solutions for fuzzy nonlinear evolution equation.

In this paper, we are going to study the existence and uniqueness solutions of fractional differential equations with fuzzy data, involving the fuzzy fractional differential operators of the order γ∈R+. The aid method of successive approximation is provided with adequate conditions for the existence and uniqueness solution. Examples are given to ex...

In this paper, the Cauchy problem of fuzzy fractional differential equations
$$
T_{\gamma}u(t) = F(t,u(t)), \quad u(t_{0})= u_{0},
$$
with fuzzy conformable fractional derivative $\bigl( \gamma$-differentiability, where $\gamma \in (0,1] \bigr)$ are introduced.
We study the existence and uniqueness of solutions and approximate solutions for the f...

In this paper, we introduce a fuzzy fractional semigroup of operators whose generator will be the fuzzy fractional derivative of the fuzzy semigroup at . We establish some of their proprieties and some results about the solution of fuzzy fractional Cauchy problem.
1. Introduction
Fractional semigroups are related to the problem of fractional power...

The aim of this work is to present the notion of a conform semi-dynamical system, unlike the concept of a dynamical system, here we can work with the continuous functions. Some examples are presented to illustrate the result of the autonomous case.

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the exi...

In this paper, the fuzzy equations of mixed convection heat transfer has been introduced. The fuzzy boundary conditions for temperature is considered. We study the existence and uniqueness of fuzzy solutions, under some conditions. The results are presented and proved in terms of velocity, steram function and temperature profiles.