Related papers: Existence and Uniqueness Theorems for Sequential L…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
Under a mild Lipschitz condition we prove a theorem on the existence and uniqueness of global solutions to delay fractional differential equations. Then, we establish a result on the exponential boundedness for these solutions.
In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…
This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…
In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for {\alpha}(\in)(0,1]. In homogeneous case, we use a fractional exponential function which…
We prove existence and uniqueness of distributional, bounded, nonnegative solutions to a fractional filtration equation in ${\mathbb R}^d$. With regards to uniqueness, it was shown even for more general equations in [19] that if two bounded…
Let $\alpha\in\,]0,1[$. We prove that the existence of the conformable fractional derivative $T_{\alpha}f$ of a function $f:[0,\infty[\,\longrightarrow \mathbb{R}$ introduced by Khalil et al. in [R. Khalil, M. Al Horani, A. Yousef, M.…
This paper presents a self-contained new theory of weak fractional differential calculus and fractional Sobolev spaces in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a…
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…
A method, recently advanced as the conformable Euler method, a general method for the finite difference discretization of fractional initial value problems for fractions in (0, 1], is shown to be valid only for the integer derivative. The…
Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
We consider a new fractional impulsive differential hemivariational inequality which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework.…
The solutions of traditional fractional differential equations neither satisfy group property nor generate dynamical systems, so the study on hyperbolicity is in blank. Relying on the new proposed conformable fractional derivative, we…
We continue the development of the basic theory of generalized derivatives as introduced in \cite{JPA} and give some of their applications. In particular, we formulate versions of a weak maximum principle, Rolle's theorem, the Mean value…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…