Solvability of Fractional Boundary Value Problems for a Combined Caputo Derivative

Abstract

This paper deals with a class of boundary value problems of the combined Caputo fractional differential equations. The main feature of the combined Caputo fractional derivative is that it holds both left and right nonlocal memory effects. By using the fractional Gronwall-type inequalities and some fixed point theorems, we established some necessary conditions for the existence of solutions. Various examples are given to show the applications of the results.

Keywords

• Combined Caputo derivative
• Existence
• Fixed point

References

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