Abstract
In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of orders 0<vartheta leq 1 and 1<vartheta leq 2. We structure the equivalent fractional integral equations of the proposed problems. Further, the existence and uniqueness theorems are proved with the aid of fixed point theorems of Krasnoselskii and Banach. Lastly, the paper includes pertinent examples to justify the validity of the results.
Highlights
Fractional calculus [1,2,3] has continued to attract the attention of many authors in the past three decades
Some investigators have recognized that innovation for novel fractional derivatives (FDs) with various nonsingular or singular kernels is necessary to address the need to model more realistic problems in various areas of engineering and science
The existence and uniqueness of solutions for different classes of fractional differential equations (FDEs) with initial or boundary conditions have been studied by several researchers; see [30,31,32,33,34,35,36,37,38] and the references therein
Summary
Fractional calculus [1,2,3] has continued to attract the attention of many authors in the past three decades. The existence and uniqueness of solutions for different classes of fractional differential equations (FDEs) with initial or boundary conditions have been studied by several researchers; see [30,31,32,33,34,35,36,37,38] and the references therein. The proposed problems are more general, and the results generalize those obtained in recent studies; we provide an extension of the development of FDEs involving this new operator.
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