New result concerning nonlocal conformable fractional differential equations of neutral type with measure of noncompactness

  • Najat CHEFNAJ Laboratory of Applied Mathematics and Scientific Calculus Sultan Moulay Slimanne University,Beni Mellal
  • Khalid HILAL Université Sultan Moulay Slimane, Beni Mellal
  • Ahmed KAJOUNI Université Sultan Moulay Slimane, Beni Mellal

Abstract

In this paper, we demonstrate the existence results of a solution for a class of initial value problems involving conformable derivatives with nonlocal conditions. The main result is established using a fixed point theorem attributed to Darbo-Sadovskii combined with semigroup theory.

Downloads

Download data is not yet available.

Author Biography

Khalid HILAL, Université Sultan Moulay Slimane, Beni Mellal

.

References

T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.

T. Abdeljawad, J. Alzabut, F. Jarad, A generalized Lyapunov-type inequality in the frame of conformable derivatives. Advances in Difference Equations, vol. 2017, no.1, pp. 1-10, 2017..

J. Banas, K. Goebel, Measure of Non compactness in Banach spaces, In Lecture Notes in Pure and applied Mathematics, New York, 1980.

M. Bouaouid, M. Atraoui, K. Hilal, and S. Melliani, Fractional differential equations with nonlocal-delay condition, Journal of Advanced Mathematical Studies, vol. 11, pp. 214- 225, 2018.

N. Chefnaj, A. Taqbibt, K. Hilal, S. Melliani, Study of nonlocal boundary value problems for hybrid differential equations involving ψ-Caputo fractional derivative with measures of noncompactness. Journal of Mathematical Sciences, pp. 1-10, 2023.

P. Chen and Y. Li, Monotone iterative technique for a class of semilinear evolution equations with nonlocal conditions, Results in Mathematics, vol. 63, no. 3-4, pp. 731-744, 2013.

K. Deimling , Nonlinear Functional Fnalysis, Springer-Verlag, New York, USA, 1985.

K. Ezzinbi, X. Fu, Existence and regularity of solutions of some neutral partial differential equations with nonlocal conditions , Nonlinear Analysis,vol. 57, no. 7, pp. 1029-1041, 2004.

H. P. Heinz, On the behaviour of measures of noncompactness with respect to differentiation and integration of vectorvalued functions, Nonlinear Analysis: Theory, Methods and Applications, vol. 7, no. 12, pp. 1351-1371, 1983.

K. Hilal, A. Kajouni, N. Chefnaj Existence of Solution for a Conformable Fractional Cauchy Problem with Nonlocal Condition,International Journal of Differential Equations, vol. 2022, p. 9, 2022.

A. Kajouni, A. Chafiki, K. Hilal et M. Oukessou A New Conformable Fractional Derivtive and Applications, International Journal of Differential Equations, vol. 2021, p. 5, 2021.

R. Khalil, M. Al Horani, A. Yousef, And M. Sababheh, A New definition Of Fractional Derivative, Journal Of Computational And Applied Mathematics, vol. 264, pp. 65-70, 2014.

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amesterdam, Netherlands, 2006.

Y. Li, Existence of solutions of initial value problems for abstract semilinear evolution equations, Acta Mathematica Sinica-Chinese Edition, vol. 48, pp. 1089-1094, 2005.

K. S. Miller, An Introduction to Fractional Calculus and Fractional Differential Equations, J. Wiley and Sons, New York, 1993.

W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Applied Mathematics Letters, vol. 10, no. 3, pp. 89-94, 1997.

A. PAZY, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag. New York,Berlin,Heidelberg;Tokyo. 1983.

S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives theory and Applications, Gordon Breach Science Publishers, Amsterdam, Netherlands, 1993.

K. Shah, T. Abdeljawad, F. Jarad, Q. Al-Mdallal, On nonlinear conformable fractional order dynamical system via differential transform method. CMES-Computer Modeling in Engineering Sciences, vol. 136, no 2, pp. 1457-1472, 2023.

Published
2025-04-15
Section
Research Articles