Geodesic
Hybrid fractional differential equation with nonlocal and impulsive conditions
Filomat, Tome 37 (2023) no. 10, p. 3291

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DOI

In this paper, we have studied the existence of solutions of the following nonlinear ψ-Hilfer hybrid fractional differential equation with non-local and impulsive conditions (non-local impulsive ψ- HHFDE)- HDα,σ,ψ0+ ( u(t) f (t,u(t)) + 1(t,u(t)) ) = h(t,u(t)), t ∈ J = [0, b] {t1, t2, ..., tn} ∆I1−ζ;ψ0+ [ u(tk) f (tk ,u(tk)) + 1(tk,u(tk)) ] = Γk ∈ R, k ∈ {1, 2, ...,n} I1−ζ;ψ0+ ( u(t) f (t,u(t)) ) t=0 + χ(u) = µ ∈ R Where 0 α 1, 0 σ 1, ζ = α + σ(1 − α), f ∈ C(J × R,R∗), χ ∈ C(R,R) and 1, h ∈ C(J × R,R). The used tools in this article are the classical technique of Dhage fixed point theorem. Further, an example is provided to illustrate our results.
DOI : 10.2298/FIL2310291H
Classification : 26A33, 34G20
Keywords: Hybrid fractional differential equation, ψ-Hilfer derivative, non-local conditions, impulsive conditions, Existence of solution, nonlinear fractional differential equations 
Khalid Hilal; Ahmed Kajouni; Samira Zerbib. Hybrid fractional differential equation with nonlocal and impulsive conditions. Filomat, Tome 37 (2023) no. 10, p. 3291 . doi: 10.2298/FIL2310291H
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     author = {Khalid Hilal and Ahmed Kajouni and Samira Zerbib},
     title = {Hybrid fractional differential equation with nonlocal and impulsive conditions},
     journal = {Filomat},
     pages = {3291 },
     year = {2023},
     volume = {37},
     number = {10},
     doi = {10.2298/FIL2310291H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2310291H/}
}
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