Related papers: Initial, inner and inner-boundary problems for a f…

In this article, we obtain existence and uniqueness results to some problems involving complex nonlinear fractional differential equations (FDEs) in the closed unit disc of C. By help of these results, we prove that some IVPs for some…

This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

In this work a classical derivation of fractional order circuits models is presented. Generalized constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next the Kirchhoff…

In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of…

We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary.…

In this work, we obtain a Lyapunov-type and a Hartman-Wintner-type inequalities for a linear and a nonlinear fractional differential equation with generalized Hilfer operator subject to Dirichlet-type boundary conditions. We prove existence…

This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…

The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…

The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…

In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…

We present sufficient conditions for the existence of positive solutions for a class of fractional singular boundary value problems in presence of Caputo fractional derivative. Further, the nonlinearity involved has singularity with respect…

The aim of this study to investigate the existence of solutions for the following nonlocal integral boundary value problem of Caputo type fractional differential inclusions. To achieve our goals, we take advantage of fixed point theorems…

In this work we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional…

We begin with a brief overview of the most commonly used fractional derivatives, namely the Caputo and Riemann-Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann-Liouville derivative,…

The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…

In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…

The mixed problem for a degenerate high order equation with a fractional derivative in a rectangular domain is considered in the article. The existence of a solution and its uniqueness are shown by the spectral method.