Abstract
We study two cases of nabla fractional Caputo difference equations. Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations. In addition, we develop the existence results for delta fractional Caputo difference equations, which correct ones obtained in Chen and Zhou. We present two examples to illustrate our main results.
Highlights
Discrete fractional calculus, allowing difference operators to have noninteger orders, can be regarded as a general concept of difference calculus
Xie et al [10] studied multiple solutions for a fractional difference boundary value problem (BVP) by a variational approach
0 < ν ≤ 1 Having established the preliminary results for Caputo operators, we consider existence and uniqueness of solutions for nonlinear Caputo fractional difference equations of the form
Summary
Discrete fractional calculus, allowing difference operators to have noninteger orders, can be regarded as a general concept of difference calculus. Lemma 2.4 (See [5, Theorem 3.119]) Let f : Na−N+1 → R . 3. Nabla case, 0 < ν ≤ 1 Having established the preliminary results for Caputo operators, we consider existence and uniqueness of solutions for nonlinear Caputo fractional difference equations of the form
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