Abstract: In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monot...

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered he...

In this article, we provide sufficient conditions for the non-existence of solutions of the boundary-value problems with fractional derivative of order α ∈ (2, 3) in the Riemann-Liouville sense D 0+x(t) + λa(t)f(x(t)) = 0, t ∈ (0, 1), x(0) = x′(0) = x′(1) = 0, and in the Caputo sense Dx(t) + f(t, x(t)) = 0, t ∈ (0, 1), x(0) = x′(0) = 0, x(1) = λ Z 1

We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual.

A fractional wave equation with a Riemann–Liouville derivative is considered. An arbitrary self-adjoint operator discrete spectrum was taken as the elliptic part. We studied inverse problem of determining order time derivative. By setting value projection solution onto first eigenfunction at fixed point in an additional condition, uniquely restored. The abstract allows us to include many models...

A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Riemann-Liouville fractional derivative of order 2 − δ with 0 < δ < 1. It is shown that any solution of such a problem can be expressed in terms of solutions to two associated weakly singular Volterra integral equations of the second kind. As a consequence, existence...

We investigate the existence of positive solutions a Riemann-Liouville fractional differential equation with sequential derivatives, parameter and nonnegative singular nonlinearity, supplemented integral-multipoint boundary conditions which contain derivatives various orders Riemann-Stieltjes integrals. Our general cover some symmetry cases for unknown function. In proof our main result, we use...

The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context fractional-order operators (integrals derivatives). extension performed presented for univariate functions, with aim determining whole set functions satisfying some constraints expressed terms integrals derivatives non-integer order. objective these expressions to so...

We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional S...

We extend the classical treatment of the Ince equation to include the effect of a fractional derivative term of order a > 0 and amplitude c. A Fourier expansion is used to determine the eigenvalue curves að Þ in function of the parameter , the stability domains, and the periodic stable solutions of the fractional Ince equation. Two important observations are the detachment of the eigenvalue cur...