Abstract
In this paper, we study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate the application of our main results.
Highlights
Fractional differential equations have gained much importance and attention due to the fact that they have been proved to be valuable tools in the modeling of many phenomena in engineering and sciences such as physics, mechanics, economics, biology, etc
Different kind of fixed point theorems are widely used as fundamental tools to prove the existence and uniqueness of solutions for various classes of fractional differential equations; for example, we refer the reader to [1,2,3,4,9,12,14,15,17,18,21,25,27] and the references cited therein
Some mathematicians considered Caputo fractional differential equations with a nonlinear term depending on the Caputo derivative
Summary
Fractional differential equations have gained much importance and attention due to the fact that they have been proved to be valuable tools in the modeling of many phenomena in engineering and sciences such as physics, mechanics, economics, biology, etc. (see, for example, [16,19,23,24] and references therein). Different kind of fixed point theorems are widely used as fundamental tools to prove the existence and uniqueness of solutions for various classes of fractional differential equations; for example, we refer the reader to [1,2,3,4,9,12,14,15,17,18,21,25,27] and the references cited therein. Motivated by the above papers, in this paper, we establish various existence and uniqueness results of solutions for a boundary value problem of nonlinear fractional differential equations of order α ∈ We add a conclusion to the paper in the last section
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