Existence and uniqueness for a fractional differential equation involving Atangana-Baleanu derivative by using a new contraction
Keywords:
Atangana-Baleanu fractional derivative, orbitally complete, fixed pointAbstract
In this study, by using some new contractions, we obtain an existence and uniqueness conclusion for a fractional differential equation with Atangana-Baleanu derivative as follows: $$ \begin{array}{rl}\label{202} (_0^{ABC}D^{\kappa}\delta)(s)&=h(s,\delta(s)),~~~~~~~~~~~~~~~~~ s\in J,~0\leq\kappa\leq 1,~~~~~~~~~~~~~~~~\\ \nonumber &\delta(0)=\delta_0,~~~~~~~~~~~~~~~~~ \end{array} $$ where \(D^{\varsigma}\) is the Atangana-Baleanu derivative of order \(\varsigma\) and \(f\) is continuous with \(f(0,\hslash(0))=0\).References
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