相关论文: A Short Note on Lyapunov Type Inequalities for Hil…
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…
We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's…
We study some functionals associated with a process driven by a fractional boundary value problem (FBVP for short). By FBVP we mean a Cauchy problem with boundary condition written in terms of a fractional equation, that is an equation…
In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial…
In this paper, we consider a nonlocal boundary-value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional derivative in a rectangular domain. The main target of this work is to analyze the uniqueness and the…
This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives with nonlocal boundary conditions. We investigate the Green function and some of its…
We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…
We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler…
We consider the discrete, fractional operator $\left(L_a^\nu x\right) (t) := \nabla [p(t) \nabla_{a^*}^\nu x(t)] + q(t) x(t-1)$ involving the nabla Caputo fractional difference, which can be thought of as an analogue to the self-adjoint…
In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rectangular domains solutions is obtained in the form of the…
In this paper we investigate fractional differential equations with Hilfer fractional derivative of order $1<\gamma<2$ and type $\delta \in [0,1]$ in a Banach space. We introduce a family of general fractional cosine operator functions of…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\]…
In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order $\alpha\in(2,3)$, involving a general form of fractional derivative. First, we prove an…
Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability…
In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the…
In this paper, we consider a nonlocal fractional boundary value problem with Prabhakar derivative and obtained a Hartman-Wintner type inequality for it.
This paper presents a new technique to investigate the existence of solutions to fractional three-point boundary value problems at resonance in a Hilbert space. Based on the proposed method, the restricted conditions…