Find in Library

In this paper, using a fixed point method, we proved the existence and uniqueness of solutions for a backward differential equation with time advance via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>−</mo></mrow></semantics></math></inline-formula>Caputo fractional derivative. Furthermore, the Ulam–Hyers–Rassias and the Ulam–Hyers stabilities of the backward differential equation with time advance via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>−</mo></mrow></semantics></math></inline-formula>Caputo fractional derivative are investigated. Finally, some experiments are given to illustrate the theoretical results.