Nonlocal boundary value problems for functional  hybrid differential equations involving  generalized  w-Caputo fractional operator

Hayat Malghi; Khalid Hilal; Prof. Ali El  Mfadel; Abdelaziz Qaffou

doi:10.5269/bspm.64298

Hayat Malghi Sultan Moulay Slimane University
Khalid Hilal Sultan Moulay Slimane University
Prof. Ali El Mfadel Sultan Moulay Slimane University https://orcid.org/0000-0002-2479-1762
Abdelaziz Qaffou Sultan Moulay Slimane University

Resumo

In this manuscript , we establish the existence and uniqueness of solutions for boundary value problems of nonlinear hybrid fractional differential equations involving generalized $\omega-$Caputo fractional derivatives. The proofs are based on Krasnoselskii fixed point theorem and some basic concept of $\omega-$Caputo fractional analysis. As application, an nontrivial example is given in the last part of this paper to illustrate our theoretical results.

Downloads

Não há dados estatísticos.

Biografia do Autor

Hayat Malghi, Sultan Moulay Slimane University

Laboratory of Applied Mathematics and Scientific Computing

Khalid Hilal, Sultan Moulay Slimane University

Laboratory of Applied Mathematics and Scientific Computing

Referências

R. P. Agarwal, S. K. Ntouyas, B. Ahmad and A. K. Alzahrani. Hadamard-type fractional functional differential equations and inclusions with retarded and advanced arguments. Advances in Difference Equations. 1, 1–15 (2016).

R. P. Agarwal, S. Hristova and D. O’Regan. A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Fract. Calc. Appl. Anal. 19 , 290–318 (2016).

R. P. Agarwal, Y. Zhou, J. Wang and X. Luo. Fractional functional differential equations with causal operators in Banach spaces. Mathematical and Compututer Modelling. 54 1440–1452 (2011).

R. Almeida. Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul.44, 460–481 (2017) .

R. Almeida, A. B. Malinowska, and M. T. T. Monteiro. Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications. Mathematical Methods in the Applied Sciences. 41(1) , 336– 352(2018).

D. Baleanu, H. Jafari, H. Khan and S. J Johnston. Results for mild solution of fractional coupled hybrid boundary value problems. Open Math.13, 601–608 (2015).

D. Baleanu, H. Khan, H. Jafari and R. A. Alipour. On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions. Advances in Difference Equations. 1, 1–14 (2015).

A. Belarbi, M. Benchohra, A. Ouahab. Uniqueness results for fractional functional differential equations with infinite delay in Frechet spaces. Appl. Anal. 58 1459–1470 (2006).

M. Caputo. Linear models of dissipation whose Q is almost frequency independent. International Journal of Geographical Information Science. 13(5), 529–539(1967).

B. C. Dhage. On β−condensing mappings in Banach algebras. Math. Student 63146–152 (1994).

B. C. Dhage. On a fixed point theorem in Banach algebras with applications. Appl. Math. Lett. 18, 273–280 (2005).

B. C. Dhage and V. Lakshmikantham. Basic results on hybrid differential equations. Nonlinear Anal. Hybrid 4, 414–424 (2010).

K. Diethelm. The Analysis of Fractional Differential Equations. Springer-Verlag, Berlin, (2010).

J. W. Green, and F. A. Valentine, On the arzela-ascoli theorem, Mathematics Magazine, 34,199–202(1961).

A. El Mfadel, S. Melliani, M. Elomari New existence results for nonlinear functional hybrid differential equations involving the ω−Caputo fractional derivative. Results in Nonlinear Analysis 5, 78-86 (2022) .

A. El Mfadel, S. Melliani and M. Elomari, Existence and uniqueness results for Caputo fractional boundary value problems involving the p-Laplacian operator. U.P.B. Sci. Bull. Series A. 84(1), 37–46 (2022).

A. El Mfadel, S. Melliani and M. Elomari, Existence results for nonlocal Cauchy problem of nonlinear ω−Caputo type fractional differential equations via topological degree methods, Advances in the Theory of Nonlinear Analysis and its Application, 6(2),270–279 (2022) .

K. Hilal, A. Kajouni. Boundary value problems for hybrid differential equations with fractional order. Advances in Difference Equations, (2015).

R. Hilfer. Applications of Fractional Calculus in Physics .Singapore. (2000).

T. L. Guo and M. Jiang. Impulsive fractional functional differential equations. Comput. Math. Appl.64, 3414–3424(2012).

A. A. Kilbas, H. M. Srivastava and J. J. Trujillo. Theory and Applications of Fractional Differential Equations. NorthHolland Mathematical studies 204. Ed van Mill. Amsterdam.( 2006). Elsevier Science B.V. Amsterdam, (2006).

Y. Luchko and J.J. Trujillo. Caputo-type modification of the Erdelyi-Kober fractional derivative. Fract. Calc. Appl. Anal. 10, 249–267 ( 2007).

F. Mainardi. Fractals and Fractional Calculus Continuum Mechanics Springer Verlag.(1997).

I. Podlubny. Fractional Differential Equations. Mathematics in Science and Engineering. Academic Press. New York. (1999).

J. Schauder. Der Fixpunktsatz in Functionalraiumen. Studia Math. 2, 171–180(1930).

Y. Zhao, S. Sun, Z. Han and Li, Q.: Theory of fractional hybrid differential equations. Comput. Math. Appl. 62(13), 12-1324 (2011).