Nonlocal boundary value problems for ?-Hilfer fractional-order Langevin equations

Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

and Applied Analysis 3 involving fractional differential equations the same applies to the boundary value problems of fractional differential equations . Moreover, the Caputo derivative for a constant is zero while the Riemann-Liouville fractional derivative of a constant is nonzero. For more details, see 17 . Lemma 2.4 see 28 . For q > 0, the general solution of the fractional differential equ...

Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations

and Applied Analysis 3 2. Background Materials and Lemmas For the convenience of the readers, in this section, we provide definitions of RiemannLiouville fractional integral and fractional derivative and some of their basic properties which will be helpful in the forth coming investigations. Definition 2.1 see 2, 5 . For a function φ : a,∞ → R, the Riemann-Liouville fractional integral of order...

On Nonlocal Integral Boundary Value Problems for Impulsive Nonlinear Differential Equations of Fractional Order

Abstract. In this paper, we investigate the existence and uniqueness of solutions for impulsive nonlinear differential equations of fractional order with nonlocal integral boundary condition. Our results are based on some suitable fixed point theorems. An illustrative example is presented.

Solvability of Nonlocal Fractional Boundary Value Problems

On four-point nonlocal boundary value problems of nonlinear impulsive equations of fractional order

Abstract: This paper is motivated from some recent papers treating the boundary value problems for impulsive fractional differential equations. We first give some notations, recall some concepts and preparation results. Second, we establish a general framework to find the solutions for impulsive fractional boundary value problems, which will provide an effective way to deal with such problems. ...