This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety derivative operators and conditions. Our work deals Caputo, Riemann-Liouville, ?-Caputo, ?-Hilfer, hybrid, Caputo-Fabrizio, Hadamard, Katugampola, Hilfer-Katugampola, p-Laplacian, proportional operators.

A system of nonlinear fractional differential equations with the Riemann–Liouville derivative is considered. Lipschitz stability in time for studied defined and studied. This connected singularity at initial point. Two types derivatives Lyapunov functions among are applied to obtain sufficient conditions property. Some examples illustrate results.

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

An approximate analytical solution of transient diffusion equation with space-fractional Riemann–Liouville fractional derivative has been developed. The integral-balance method and an assumed parabolic profile with undefined exponent have been used. The spatial correlation the superdiffusion coefficient in potential power-law form has been discussed. The laws of the spatial and temporal propaga...

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...

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problemD0 u t μa t f t, u t , 0 < t < 1, u 0 u 1 u ′ 0 u′ 1 0, where μ > 0, a, and f are continuous, α ∈ 3, 4 is a real number, and D0 is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to ill...

where 2 < a, b ≤ 3, 0 < ξ1 <... < ξm <1, 0 < h1 <... < hm <1, 0 <g1 <... < gm <1, 0 < δ1 <... < δm <1, ai, bi, cj, dj Î R, f, g : [0, 1] × R 3 ® R, f, g satisfies Carathéodory conditions, Dα0+ and I α 0+ are the standard Riemann-Liouville fractional derivative and fractional integral, respectively. Wang et al. Advances in Difference Equations 2011, 2011:44 http://www.advancesindifferenceequatio...

As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...