Abstract
We study a new class of boundary value problems of nonlinear fractional differential equations whose nonlinear term depends on a lower-order fractional derivative with fractional separated boundary conditions. Some existence and uniqueness results are obtained by using standard fixed point theorems. Examples are given to illustrate the results.
Highlights
We study the existence and uniqueness of solutions for a class of fractional differential equations whose nonlinear term f depends on the lower-order fractional derivative of the unknown function x(t) with the fractional separated boundary conditions given by
The subject of fractional differential equations has emerged as an important area of investigation
It is clear that the problem ( ) has solutions if and only if the operator equation X as (F x) = x has fixed points
Summary
We study the existence and uniqueness of solutions for a class of fractional differential equations whose nonlinear term f depends on the lower-order fractional derivative of the unknown function x(t) with the fractional separated boundary conditions given by Where cDq denotes the Caputo fractional derivative of order q, f is a continuous function on [ , T] × R × R and ai, bi, ci, i = , are real constants with a = and T > . Α x( ) + β cDpx( ) = γ , α x( ) + β cDpx( ) = γ , < p < , where cDq denotes the Caputo fractional derivative of order q, f is a given continuous function and αi, βi, γi (i = , ) are real constants, with α = .
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