This work investigates the existence and uniqueness of solutions for a coupled system fractional differential equations with three-point generalized integral boundary conditions within proportional derivatives Riemann-Liouville type. By using Schauder Banach fixed point theorems, we study aforesaid system. Finally, present an example to validate our theoretical outcomes.

In this article we present the notions of adjoint differential expressions for fractional-order differential expressions, adjoint boundary conditions for fractional differential equations, and adjoint fractional-order operators. These notions are based on new formulas obtained for various types of fractional derivatives. The introduced notions can be used in many fields of modelling and control...

In this paper, we study the existence of positive solutions for a system fractional differential equations with ?-Laplacian operators, Riemann–Liouville derivatives diverse orders and general nonlinearities which depend on several integrals differing orders, supplemented nonlocal coupled boundary conditions containing Riemann–Stieltjes varied derivatives. The from are continuous nonnegative fun...

The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fracti...

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate corresponding inverse problems. Our goal is to determine variable from exterior partial measurements of Dirichlet-to-Neumann map. exploit integration by parts formula for Riemann-Liouville Caputo derivatives derive Runge approximation property our operator based on unique continuation Lapl...

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

Abstract. Based on the fractional q–integral with the parametric lower limit of integration, we define fractional q–derivative of Riemann–Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .

In this paper, using the Riemann-Liouville fractional q-integral, we establish some new fractional integral inequalities by using two parameters of deformation q1 and q2.

We compare the Riemann–Liouville fractional integral (fI) of a function f(z) with the Liouville fI of the same function and show that there are cases in which the asymptotic expansion of the former is obtained from those of the latter and the difference of the two fIs. When this happens, this fact occurs also for the fractional derivative (fD). This method is applied to the derivation of the as...