The main goal of this study is to demonstrate an existence result a coupled implicit Riemann-Liouville fractional integral equation. First, we prove new fixed point theorem in spaces with extended norm structure. That generalized Darbo’s associated the vector Kuratowski measure noncompactness. Second, employ our obtained investigate solutions equation on Banach space C([0,1],R)×C([0,1],R).

and Applied Analysis 3 Definition 2.2 see 18 . The standard Riemann-Liouville fractional derivative of order α > 0 of a continuous function y : a,∞ → R is given by D a y t 1 Γ n − α ( d dt )n ∫ t a t − s n−α−1y s ds, 2.2 where n α 1, provided that the integral on the right-hand side converges. Definition 2.3 see 18 . The Riemann-Liouville fractional integral of order α > 0 of a function y : a,∞...

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, apply Schaefer’s fixed point theorem. Furthermore, present Lyapunov inequality for corresponding problem.

<p>This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating Riemann-Liouville fractional derivative operator. These are derived by utilizing forthright computations, so-called weighted mean value theorem (WMVT). Undoubtedly, such will be extremely useful establishing approaches several ...

In this paper, we establish some new integral inequalities for convex functions by using the Riemann-Liouville operator of non integer order. For our results some classical integral inequalities can be deduced as some special cases.

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

Using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations whi...

This work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, novel three-point formula approximating the Riemann–Liouville integrator is established, and then it applied to generate approximate solutions Such derived use of generalized Taylor theorem coupled recent definition definite integral. Our compared solution generated by Euler...