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In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper, we use Krasnoselskii's fixed point theorem to study the existence and uniqueness of periodic solutions of a class of iterative differential equation... where K 2 R \ {0},ai 2 R, fi(t) denotes ith iterate of f (t), i = 1,2, . . ., n. The above equation is closely related to a discrete derivatives sequence F0(m) (see [Y.-F.S. P'etermann, Jean-Luc R'emy, Ilan Vardi, Discrete derivatives of sequences, Adv. in Appl. Math. 27 (2001) 562-584]). [ABSTRACT FROM AUTHOR]

In this paper we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this we extend the model describing the Rubella spread by changing the derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative. [ABSTRACT FROM AUTHOR]

In view of the Avery-Peterson fixed point theorem, this paper investigates the existence of three positive solutions for the second-order boundary value problem with integral boundary conditions The interesting point is that the nonlinear term involves the first-order derivative explicitly. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlinear three-point boundary value problem of fractional differential equations with boundary conditions involving Riemann-Liouville fractional derivatives $D^{\alpha}_{0^{+}}$ and $D^{\beta}_{0^{+}}$, where $a(t)$ maybe singular at $t=0$ or $t=1$. We use the Banach contraction mapping principle and the Leggett-Williams fixed point theorem to obtain the existence and uniqueness of positive solutions and the existence of multiple positive solutions. We investigate the above fractional differential equations without many preconditions by the fixed point index theory and obtain the existence of a single positive solution. Some examples are given to show the applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and multiplicity results of positive solutions for a boundary value problem of nonlinear fractional differential equations. The differential operator is taken in the Riemann-Liouville sense and the nonlinear term depends on the fractional derivative of an unknown function. We derive first the associated Green's function and prove its properties. Consequently, the considered problem is deduced to an equivalent integral equation. Next, by means of the Leggett-Williams fixed point theory, we obtain the existence and multiplicity results of positive solutions. [ABSTRACT FROM AUTHOR]

In this paper, by employing two fixed point theorems of a sum operators, we investigate the existence and uniqueness of positive solutions for the following fractional boundary value problems: $-D_{0+}^{\alpha}x(t)=f(t, x(t), x(t))+g(t, x(t))$, $0< t <1$, $1< \alpha<2$, where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative, subject to either the boundary conditions $x(0)=x(1)=0$ or $x(0)=0$, $x(1)=\beta x(\eta)$ with $\eta, \beta\eta^{\alpha-1} \in(0,1)$. We also construct an iterative scheme to approximate the solution. As applications of the main results, two examples are given. [ABSTRACT FROM AUTHOR]