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).

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

where D , D , and D are the standard Riemann-Liouville fractional derivatives, I and I are the Riemann-Liouville fractional integrals, and 0 < γ < 1 < β < 2 < α < 3, ν,ω > 0, 0 < η, ξ < 1, k ∈R, f ∈ C([0, 1]×R×R,R), g ∈ C([0, 1]×R,R). The p-Laplacian operator is defined as φp(t) = |t|p–2t, p > 1, and (φp) = φq, 1 p + 1 q = 1. The study of boundary value problems in the setting of fractional cal...

In this paper, we consider a new class of boundary value problems of Caputo type fractional differential equations supplemented with classical/nonlocal Riemann-Liouville integral and flux boundary conditions and obtain some existence results for the given problems. The flux boundary condition x′(0) = b cDβx(1) states that the ordinary flux x′(0) at the left-end point of the interval [0, 1] is p...

The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinear fractional partial differential equations. By means of this method, the space-time fractional generalized Hirota-Satsuma coupled Kortewegde Vries equations are successfully solved. As a result, three types...

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for th...

In this paper, the Caputo time varying singular fractional differential systems with delay and the Riemann-Liouville time varying singular fractional differential systems with delay are considered . By the D− inverse matrix and α − δ function, two fundamental solutions are given. The variation formulae for time varying singular fractional differential systems with delay are obtained. Mathematic...

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability solutions a coupled system fractional differential equations with Erdélyi–Kober Riemann–Liouville integral boundary conditions. Banach fixed point theorem used prove uniqueness solutions, while Leray–Schauder alternative existence solutions. Furthermore, we conclude that solution discussed problem Hyer...