Abstract
This paper is concerned with a class of anti-periodic boundary value problems for fractional differential equations with the Riesz–Caputo derivative, which can reflected both the past and the future nonlocal memory effects. By means of new fractional Gronwall inequalities and some fixed point theorems, we obtain some existence results of solutions under the Lipschitz condition, the sublinear growth condition, the nonlinear growth condition and the comparison condition. Three examples are given to illustrate the results.
Highlights
1 Introduction Fractional calculus goes back to Newton and Leibniz in the seventeenth century. It is a generalization of ordinary differential equations and integration to arbitrary non-integer order [1]
Uniqueness and stability of initial value problems are the main topics of fractional differential equations; see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23] and the references therein
Baleanu et al [7,8,9] investigated the existence of solutions for fractional differential equations including the Caputo-Fabrizio derivative
Summary
Fractional calculus goes back to Newton and Leibniz in the seventeenth century. It is a generalization of ordinary differential equations and integration to arbitrary non-integer order [1]. Zhou et al [5, 6] obtained some existence and uniqueness results of fractional differential equations. Baleanu et al [7,8,9] investigated the existence of solutions for fractional differential equations including the Caputo-Fabrizio derivative.
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