TY  - JOUR
T1  - Measure of Noncompactness for Nonlinear Hilfer Fractional Differential Equation in Banach Spaces
AU  - Benbachır, Maamar
AU  - Boutiara, Abdellatif
AU  - Guerbati, Kaddour
PY  - 2019
DA  - October
Y2  - 2020
JF  - Ikonion Journal of Mathematics
JO  - ikjm
PB  - Nihat AKGÜNEŞ
WT  - DergiPark
SN  - 2687-6531
SP  - 55
EP  - 67
VL  - 1
IS  - 2
LA  - en
AB  - This paper deals with nonlinear fractional differential equation with boundary value problemconditions. We investigate the existence of solutions in Banach spaces with Hilfer derivative.To obtain such result we apply Monch's fixed point theorem and the technique of measures ofnoncompactness. An example illustrating the theory is given.
KW  - Fractional differential equation
KW  - Hilfer fractional derivative
KW  - Kuratowski measures of noncompactness
CR  - S. Abbas, M. Benchohra, M. Bohner, Weak Solutions for Implicit Differential Equations
with Hilfer-Hadamard Fractional Derivative, Advances in Dynamical Systems and Applications,
Volume 12, Number 1, pp. 1-16 (2017)
CR  - S. Abbas, M. Benchohra, J.E. Lazreg, J. J. Nieto, On a coupled system of Hilfer and
Hilfer-Hadamard fractional deerential equation in Banach spaces, J. Nonlinear Funct.
Anal. 2018 (2018), Article ID 12.
CR  - D. Vivek, K. Kanagarajan, S. Sivasundaram, On the behavior of solutions of Hilfer-
Hadamard type fractional neutral pantograph equations with boundary conditions, Communications
in Applied Analysis, 22, No. 2 (2018), 211-232.
CR  - J.-R. Wang, Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer
fractional derivative, Appl. Math. Comput. 266 (2015), 850-859.
CR  - M. Yang, Q.-R. Wang, Approximate controllability of Hilfer fractional differential inclusions
with nonlocal conditions, Math. Methods Appl. Sci. 40 (2017), 1126-1138.
UR  - https://dergipark.org.tr/en/pub/ikjm/issue//653138
L1  - https://dergipark.org.tr/en/download/article-file/920662
ER  -