## About

33

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Introduction

## Publications

Publications (33)

In this article, we consider an Itô stochastic semilinear differential equation with unknown initial state and a linear observation system. It is proved that under a certain condition on the observability Gramian, the initial state of the equation can be recovered. This result is demonstrated by an example.

In this article, we deal with fractional stochastic differential equations, so-called Caputo type fractional backward stochastic differential equations (Caputo fBSDEs, for short), and study the well-posedness of an adapted solution to Caputo fBSDEs of order α∈(12,1) whose coefficients satisfy a Lipschitz condition. A novelty of the article is that...

Sobolev‐type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate the existence of mild solutions for fractional‐order time‐delay evolution equation of Sobolev type with multiorders in a Banach space with the help of two various methods. First, we study abstract probl...

A strong inspiration for studying Sobolev-type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical processes. We introduce a novel technique for solving Sobolev-type fractional evolution equations with multi-orders in a Banach space. We propose a new Mittag-Leffler-type func...

In this paper, we obtain a closed-form representation of a mild solution to the fractional stochastic degenerate evolution equation in a Hilbert space using the subordination principle and semigroup theory. We study aforesaid abstract fractional stochastic Cauchy problem with nonlinear state-dependent terms and show that if the Sobolev type resolve...

Perturbation theory has long been a very useful tool in the hands of mathematicians and physicists. The purpose of this paper is to prove some perturbation results for infinitesimal generators of fractional strongly continuous cosine families. That is, we impose sufficient conditions such that $ A $ is the infinitesimal generator of a fractional st...

In this paper, we study the exact asymptotic separation rate of two distinct solutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs). Our goal in this paper is to establish results of the global existence and uniqueness and continuity dependence of the initial values of the solutions to Caputo SMTDEs with non-permutable mat...

Perturbation theory has long been a very useful tool in the hands of mathematicians and physicists. The purpose of this paper is to prove some perturbation results for infinitesimal generators of fractional strongly continuous cosine families. That is, we impose sufficient conditions such that $\mathscr{A}$ is the infinitesimal generator of a fract...

Our aim in this paper is to establish a new theorem on the global existence and uniqueness of adapted solution to Caputo fractional backward stochastic differential equations (for short Caputo FBSDEs) of order $\alpha \in (\frac{1}{2},1)$ under a weaker condition than Lipschitz one. The interesting point here is to apply a weighted norm in square i...

Our main result in this paper is to establish a fundamental lemma to prove the global existence and uniqueness of an adapted solution to a singular backward stochastic nonlinear Volterra integral equation (for short singular BSVIE) of order $\alpha \in (\frac{1}{2},1)$ under a weaker condition than Lipschitz one in Hilbert space.

A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution equations of order $\alpha\in (1,2]$ associated with the infinitesimal generator of an operator fractional cosine func...

The novelty of this paper is to derive a mild solution by means of recently defined Mittag-Leffler type functions of fractional stochastic Langevin equations of orders α∈(1,2] and β∈(0,1] whose coefficients satisfy standard Lipschitz and linear growth conditions. Then, we prove existence and uniqueness results of mild solution and show the coincide...

Sobolev type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate fractional-order time-delay evolution equation of Sobolev type with multi-orders in a Banach space and introduce an analytical representation of a mild solution via a new delayed Mittag-Leffler type fun...

Our aim in this paper is to establish results on the global existence and uniqueness and continuity dependence on the initial values of solutions for Caputo stochastic multi-term differential equations (for short Caputo SMTDEs) with non-permutable matrices of order $\alpha \in (\frac{1}{2},1)$ and $\beta \in (0,1)$ whose coefficients satisfy a stan...

The novelty of our paper is to establish results on asymptotic stability of mild solutions in $p$th moment to Riemann-Liouville fractional stochastic neutral differential equations (for short Riemann-Liouville FSNDEs) of order $\alpha \in (\frac{1}{2},1)$ using a Banach's contraction mapping principle. The core point of this paper is to derive the...

A strong inspiration for studying Sobolev type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical processes. We introduce a novel technique for solving Sobolev type fractional evolution equations with multi-orders in a Banach space. We propose a new Mittag-Leffler type func...

Linear systems of fractional differential equations have been studied from various points of view: applications to electric circuit theory, approximate solutions by numerical methods, and recently exact solutions by analytical methods. We discover here that, to obtain a fully closed-form solution in all cases, it is necessary to introduce a new typ...

In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type differentiation operators with general fractional-order of $n-1 <\alpha \leq n$, $n \in \mathbb{N}$ . A rule of frac...

Multi-order fractional differential equations have been studied due to their applications in
modeling, and solved using various mathematical methods. We present explicit analytical solutions for several families of Langevin differential equations with general fractional orders, both homogeneous and inhomogeneous cases. The results can be written, i...

Multi-order fractional differential equations have been studied due to their applications in modeling, and solved using various mathematical methods. We present explicit analytical solutions for several families of Langevin differential equations with general fractional orders, both homogeneous and inhomogeneous cases. The results can be written, i...

We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by putting to use of the eminent Hankel's integral. We also investigate Laplace integral relation and convolution re...

In this paper, we investigate new results on the existence and uniqueness of mild solutions to stochastic neutral differential equations involving Caputo fractional time derivative operator with Lipschitz coefficients and under some Carathéodory-type conditions on the coefficients through the Picard approximation technique. To do so, we derive a st...

In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus, we investigate new results on existence and uniqueness of mild solutions with the help of weighted maximum norm...

The novelties of this research work is to establish stability results in Ulam-Hyers sense for the nonlinear fractional stochastic neutral differential equations system with the aid of weighted maximum norm and Itô’s isometry in finite dimensional stochastic settings.

In this paper, we investigate new results on the existence and uniqueness of mild solutions to stochastic neutral differential equations involving Caputo fractional time derivative operator with Lipschitz coefficients and under some Carathéodory-type conditions on the coefficients through the Picard's approximation technique. To do so, we derive a...

Fractional differential equations have been studied due to their applications in modelling, and solved using
various mathematical methods. Systems of fractional differential equations are also used, for example in the
study of electric circuits, but they are more difficult to analyse mathematically. We present explicit solutions
for several familie...

In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic
analogue of variation of constants formula via a newly defined delayed
Mittag-Leffler type matrix function. Thus, we investigate new results
on existence and uniqueness of mild solutions with the help of weighted
maximum nor...

## Projects

Projects (6)

Perturbation theory has long been a very useful tool in the hands of mathematicians and physicists. The purpose of this work is to prove some perturbation results for infinitesimal generators of fractional strongly continuous cosine families. That is, we impose sufficient conditions such that A is the infinitesimal generator of a fractional strongly continuous cosine family in a Banach space X, and B is a bounded linear operator in X, then A + B is also the infinitesimal generator of a fractional strongly continuous cosine family in X.

Linear systems of fractional differential equations have been studied from various points of view: applications
to electric circuit theory, approximate solutions by numerical methods, and recently exact solutions by
analytical methods. Taking a particular consideration to computational techniques for multi-term differential equations in classical and fractional senses, we solved the initial value problem for a fractional differential equation with three independent orders by fractional Taylor basis vector method which based on generalized Taylor’s formula. In addition, the operational
matrix for the fractional integral operator in Riemann-Liouville’s sense is introduced and this specific
matrix is used to reduce the given fractional differential equation with initial condition to a system of
algebraic equations. From illustrative examples, we conclude that the obtained solutions by a proposed
numerical method are much closer to the exact solutions or coincide with the exact solutions. Thus, Taylor's basis vector method in a fractional sense is an accurate and effective computational tool for fractional
differential equations with multi-orders. Furthermore, we present an upper bound
of the absolute errors with the aid of the generalized Taylor formula and introduce an error estimation for fractional Taylor polynomials with the residual error function.