@article{Bendrici_Boutiara_Boumedien-Zidani_2024, title={Existence theory for $\psi$-Caputo fractional differential equations}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7669}, DOI={10.3842/umzh.v76i9.7669}, abstractNote={<p>UDC 517.9</p> <p>The target of this paper is to handle a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsuling a collective fractional derivative known as the $\psi$-Caputo fractional operator.<span class="Apple-converted-space"> </span>The applied fractional operator generated by the kernel is of the following kind: $k(t,s)=\psi (t)-\psi(s).$<span class="Apple-converted-space"> </span>The existence of the solutions of the above-mentioned equations is tackled by using Mönch’s fixed-point theorem combined with the technique of measures of noncompactness.<span class="Apple-converted-space"> </span>In addition, we discuss the problem of stability within the scope of the Ulam–Hyers stability criteria for the main fractional system.<span class="Apple-converted-space"> </span>Finally, an example is given to illustrate the viability of the reported results.</p>}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Bendrici, Nadhir and Boutiara, Abdellatif and Boumedien-ZidaniMalika}, year={2024}, month={Sep.}, pages={1291 - 1303} }