Measure of Noncompactness for Nonlinear Hilfer Fractional Differential Equation in Banach Spaces

Year 2019, Volume: 1 Issue: 2, 55 - 67, 16.10.2019

Abdellatif Boutiara , Maamar Benbachır , Kaddour Guerbati

https://izlik.org/JA64ST33ZF

Abstract

This paper deals with nonlinear fractional differential equation with boundary value problem
conditions. We investigate the existence of solutions in Banach spaces with Hilfer derivative.
To obtain such result we apply Monch's fixed point theorem and the technique of measures of
noncompactness. An example illustrating the theory is given.

Keywords

Fractional differential equation , Hilfer fractional derivative , Kuratowski measures of noncompactness

References

• 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)
• 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.
• 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.
• J.-R. Wang, Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Appl. Math. Comput. 266 (2015), 850-859.
• M. Yang, Q.-R. Wang, Approximate controllability of Hilfer fractional differential inclusions with nonlocal conditions, Math. Methods Appl. Sci. 40 (2017), 1126-1138.