In related proceedings pursuant to Family Court Act article 10, (1) the mother appeals, as limited by her brief, from so much of an order of fact-finding of the Family Court, Suffolk County (Freundlich, J.), dated February 16, 2012, as, after a hearing, found that she abused the child Robert A., and (2) the father appeals, as limited by his brief, from stated portions of an order of disposition of the same court dated February 29, 2012, which, upon the order of fact-finding dated February 16, 2012, finding, inter alia, that he had abused the child Robert A., inter alia, determined that he derivatively neglected the children Alicia A. and Ayden C., placed him under the supervision of the Suffolk County Department of Social Services for a period of one year, and directed him to have no contact with the children Alicia A. and Ayden C. for a period of one year.
Ordered that the order of fact-finding is affirmed insofar as appealed from by the mother, without costs or disbursements; and it is further,
Ordered that the father’s appeal from so much of the order of disposition as placed him under the supervision of the Suffolk County Department of Social Services for a period of one year and directed him to have no contact with the children Alicia A. and Ayden C. for a period of one year is dismissed as academic, without costs or disbursements, as the one-year period has expired; and it is further,
Ordered that the order of disposition is affirmed insofar as reviewed, without costs or disbursements.
The mother’s only contention on appeal is that the Family Court lacked subject matter jurisdiction with respect to proceeding No. 1, inasmuch as the child Robert A. was deceased and she had no other children. This contention is without merit (see Matter of Alijah C., 1 NY3d 375, 378-379 [2004]; cf. Social Services Law § 384-b [8] [b] [ii]; Family Ct Act § 1012 [e] [i]).
The father contends that the evidence at the fact-finding hearing was insufficient to support the Family Court’s finding that he abused the child Robert A. The petitioner’s medical experts opined that the rib fractures suffered by the child Robert A. had been inflicted intentionally, and the record reflects that the child was in the parents’ care when he suffered the fractures. *613Accordingly, the petitioner established a prima facie case of child abuse, and the burden shifted to the father to rebut the evidence of his culpability (see Family Ct Act § 1046 [a] [ii]; Matter of Philip M., 82 NY2d 238, 244 [1993]; Matter of Jacob B. [Rachel B.], 77 AD3d 936, 936 [2010]; Matter of Arianna L., 55 AD3d 733, 733 [2008]). The father failed to provide a reasonable and adequate explanation for the child’s injuries (see Matter of Jacob B. [Rachel B.], 77 AD3d at 936; Matter of Arianna L., 55 AD3d at 733). Moreover, contrary to the father’s contention, the Family Court’s assessment of the conflicting expert testimony, which is entitled to deference, is supported by the record, and we decline to disturb its determination (see Matter of Diamond K., 31 AD3d 553, 553-554 [2006]).
The proof that the father abused Robert A. was sufficient to establish that the children Alicia A. and Ayden C. were derivatively neglected (see Family Ct Act §§ 1012 [e] [ii]; 1046 [a] [i]; [b] [i]; Matter of Diamond K., 31 AD3d at 553-554; Matter of Jesus M., 20 AD3d 479, 480 [2005]; Matter of Marc A., 301 AD2d 595, 597 [2003]). Accordingly, there is no basis to disturb the Family Court’s determination with respect to derivative neglect. Balkan, J.E, Hall, Lott and Sgroi, JJ., concur.