In this work, a Lie group reduction for (2 + 1) dimensional fractional Kadomtsev-Petviashvili (KP) system is determined by using the symmetry method with Riemann Liouville derivative. After reducing into two-dimensional nonlinear partial differential (NLFPDEs), power series (PS) applied to obtain exact solution. Further obtained solution analyzed convergence. Then, new conservation theorem gene...

We study a coupled system of implicit differential equations with fractional-order boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, at least one solution are established by applying Banach contraction Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities discussed. An example is presented to illustrate our main result. suggested general...

This paper uses a new multiplication of fractional functions and chain rule for derivatives, regarding the Jumarie type modified Riemann-Liouville derivatives to obtain general solutions four types first order differential equations. On other hand, some examples are proposed illustrate our results.

In this study, we present a new notion of nonlocal closed boundary conditions. Equipped with these conditions, discuss the existence solutions for mixed nonlinear differential equation involving right Caputo fractional derivative operator, and left Riemann–Liouville integral operators different orders. We apply decent fruitful approach fixed point theory to establish desired results. Examples a...

In this paper, we study two stochastic problems for time-fractional Rayleigh-Stokes equation including the initial value problem and terminal problem. Here, are perturbed by Wiener process, fractional derivative taken in sense of Riemann-Liouville, source function time-spatial noise nonlinear satisfy globally Lipschitz conditions. We attempt to give some existence r...

One considers a class of fractional random processes defined as non-random dynamics subject to Gaussian white noises in coarse-grained time, according to Maruyama’s notation. After some prerequisites on modified Riemann-Liouville fractional derivative, fractional Taylor’s series and integration with respect to (dx)α , one displays the main results which are as follows: firstly, a general scheme...

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.