In this paper, we study the existence of a solution for nonlinear implicit fractional differential equation type D?u(t) = f (t, u(t),D?u(t)), with Riemann-Liouville derivative via different boundary conditions u(0) u(T), and three point ?1u(?) u(T) ?2u(?), where T > 0, t ? I [0,T], 0 < 1, T, ?1 ?2 1.

In this paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville derivative with delay and its corresponding integral equation. Under some sufficient conditions, establish the global local existence results for that problem by applying fixed point theorems. addition, have investigated continuous integrable solutions problem. Moreover, dis...

Abstract In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, define in an appropriate way initial conditions which are deeply connected the derivative used. We introduce generalization practical stability call time. Several sufficient for time obtained using Lyapunov functions and modified Razumikhin technique. Two types derivati...

In the finance market, it is well known that price change of underlying fractal transmission system can be modeled with Black-Scholes equation. This article deals finding approximate analytic solutions for time-fractional equation fractional integral boundary condition a European option pricing problem in Katugampola derivative sense. It generalizes both Riemann–Liouville and Hadamard derivativ...

Anomalous dispersion is observed throughout hydrology, yielding a contaminant plume with heavy leading tails. The fractional advection dispersion equation (FADE) captures this behavior by replacing the second-order spatial derivative with a Riemann-Liouville (RL) fractional derivative. The RL fractional derivative is a nonlocal operator and models large jumps of solute particles in heterogeneou...

In this present work, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the direct algebraic method are employed for constructing the exact complex solutions of non-linear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. Reference to this paper should be made as follows: Taghiz...

By using the coincidence degree theory, we consider the following 2m-point boundary value problem for fractional differential equationD 0 u t f t, u t , D α−1 0 u t , D α−2 0 u t e t , 0 < t < 1, I3−α 0 u t |t 0 0, Dα−2 0 u 1 ∑m−2 i 1 aiD α−2 0 u ξi , u 1 ∑m−2 i 1 biu ηi , where 2 < α ≤ 3, D 0 and I 0 are the standard Riemann-Liouville fractional derivative and fractional integral, respectively...

In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this func...

*Correspondence: [email protected] Department of Mathematics, Hefei Normal University, Hefei, Anhui 230061, China Abstract In this paper, by means of the Avery-Peterson fixed point theorem, we establish the existence result of a multiple positive solution of the boundary value problem for a nonlinear differential equation with Riemann-Liouville fractional order derivative. An example illustrating...

We present a new method of deriving a boundary condition at a thin membrane for diffusion from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with the Riemann– Liouville fractional time derivative of the 1/2 order. Such a form of the boundary condition shows that a tran...