Rezumat articol ediţie STUDIA UNIVERSITATIS BABEŞ-BOLYAI În partea de jos este prezentat rezumatul articolului selectat. Pentru revenire la cuprinsul ediţiei din care face parte acest articol, se accesează linkul din titlu. Pentru vizualizarea tuturor articolelor din arhivă la care este autor/coautor unul din autorii de mai jos, se accesează linkul din numele autorului. STUDIA MATHEMATICA - Ediţia nr.4 din 2021 Articol: POSITIVE SOLUTION OF HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS.Autori:  MOHAMMED A. ALMALAHI, SATISH K. PANCHAL, MOHAMMED S. ABDO. Rezumat:  DOI: 10.24193/subbmath. 2021.4.09Published Online: 2021-12-14Published Print: 2021-12-30pp. 709-722 VIEW PDF FULL PDF In this article, we have interested the study of the existence and uniqueness of positive solutions of the first-order nonlinear Hilfer fractional differential equation Dα,β0+y(t)=f(t,y(t)), 0 with the integral boundary condition I1−γ0+y(0)=λ∫10y(s)ds+d,I0+1−γy(0)=λ∫01y(s)ds+d, where \$0fractional differential equation into an equivalent integral equation. Then we establish sufficient conditions and employ the Schauder fixed point theorem and the method of upper and lower solutions to obtain the existence of a positive solution of a given problem. We also use the Banach contraction principle theorem to show the existence of a unique positive solution. The result of existence obtained by structure the upper and lower control functions of the nonlinear term is without any monotonous conditions. Finally, an example is presented to show the effectiveness of our main results. Mathematics Subject Classification (2010): 34A08, 34B15, 34B18, 34A12, 47H10. Keywords: Fractional differential equations, positive solution, upper and lower solutions, fixed point theorem, existence and uniqueness.