In this paper, by using the coincidence degree theory, we consider the following two-point boundary value problem for fractional differential equation { D 0+x(t) = f(t, x(t), x ′(t)), t ∈ [0, 1], x(0) = 0, x′(0) = x′(1), where D 0+ denotes the Caputo fractional differential operator of order α, 1 < α ≤ 2. A new result on the existence of solutions for above fractional boundary value problem is ...

‎in this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(vofides‎, ‎for short)‎. ‎in these equations‎, ‎the variable-order fractional integration(vofi) and‎ ‎variable-order fractional derivative (vofd) are described in the‎ ‎riemann-liouville's and caputo's sense,respectively‎. ‎numerical experiments‎, ‎consisting of two exam...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multiorder fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is ve...

We study linear fractional boundary value problems consisting of an α-th order Riemann-Liouville fractional differential equation with 2 < α ≤ 3 and certain fractional boundary conditions. We derive several Lyapunovtype inequalities and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for related homogeneous and nonhomogeneous linear fractional boundary va...

Keywords: Fractional differential equations Impulsive fractional differential equations Impulse General solution Existence a b s t r a c t In this paper, for impulsive differential equations with fractional-order q 2 ð0; 1Þ, we show that the formula of solutions in cited papers are incorrect. Secondly, we find out a formula of the general solution for impulsive Cauchy problem with Caputo fracti...

We present and discuss an algorithm for the numerical solution of nonlinear differential equations of fractional (i.e., non-integer) order. This algorithm allows us to analyze in an efficient way a mathematical model for the description of the behaviour of viscoplastic materials. The model contains a nonlinear differential equation of order β, where β is a material constant typically in the ran...