TY - JOUR
ID - 4157
TI - Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions
JO - Journal of Mathematical Modeling
JA - JMM
LA - en
SN - 2345-394X
AU - Wahash, Hanan A.
AU - Panchal, Satish K.
AU - Abdo, Mohammed S.
AD - Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India
AD - Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen
Y1 - 2020
PY - 2020
VL - 8
IS - 4
SP - 393
EP - 414
KW - Caputo fractional differential equation
KW - integral boundary condition
KW - existence of positive solution
KW - control functions
KW - Fixed point theorem
DO - 10.22124/jmm.2020.16125.1407
N2 - This article is devoted to the study of a new class of nonlinear fractional-order differential equations with integral boundary conditions involving a generalized version of the Caputo type fractional derivative with respect to another function $h$. In such a path, we transform the proposed problem into an equivalent integral equation. Then we build the upper and lower control functions of the nonlinear term without any monotone requirement except the continuity. By utilizing the method of upper and lower solutions, the fixed point theorems of Schauder and Banach, we obtain the existence and uniqueness of positive solutions for the problem at hand. Finally, we present some examples to illuminate our results.
UR - https://jmm.guilan.ac.ir/article_4157.html
L1 - https://jmm.guilan.ac.ir/article_4157_bebd828095aa4e625a009cd6ec2f6d06.pdf
ER -