In this paper, we study a new nonlinear sequential differential prob-
 lem with nonlocal integral conditions that involve convergent series. The
 problem involves two fractional order operators: Riemann-Liouville inte-
 gral, Caputo and derivatives. We prove an existence
 uniqueness result. Also, existence end our
 paper by presenting some illustrative examples.

Integral identities created in inequality theory studies help to prove many inequalities. Recently, different fractional integral and derivative operators have been used achieve these identities. In this article, with the of Atangana-Baleanu operators, an identity was first obtained various inequalities for convex functions proved using identity. last part simulation graphs are given reveal con...

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and ...

In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving ψ-Riemann–Liouville fractional derivative with nonlocal conditions. We first transformed problem into an integral then analyzed by means Banach fixed-point theorem Krasnoselskiis theorem. Some known results in literature are extended. Finally, example is given to illustrate our theoretical ...

Based on high order approximation of L-stable RungeKutta methods for the Riemann-Liouville fractional derivatives, several classes of high order fractional Runge-Kutta methods for solving nonlinear fractional differential equation are constructed. Consistency, convergence and stability analysis of the numerical methods are given. Numerical experiments show that the proposed methods are efficien...

A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs). The fractional derivative is defined in the sense ofmodified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled...