Existence of Solutions for a Fractional-Order Boundary-Value Problem

Author(s):  
I. Y. Karaca ◽  
D. Oz
2020 ◽  
Vol 72 (12) ◽  
pp. 1651-1662
Author(s):  
I. Y. Karaca ◽  
D. Oz

UDC 517.9 We investigate the existence of solutions for a fractional-order boundary-value problem by using some fixed point theorems.As applications, examples are given to illustrate the main results.


Author(s):  
Mohammed Said Souid

The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit di erential equations with integral conditions involving the Caputo fractional derivative. Our results are based on Schauder's xed point theorem and the Banach contraction principle fi xed point theorem.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid

Abstract The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.


2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nemat Nyamoradi ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal

We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusionD0+αut+Ft,ut,u′t∋0,0<t<+∞,u0=u′0=0,Dα-1u+∞-∑i=1m-2‍βiuξi=0, whereD0+αis the standard Riemann-Liouville fractional derivative,2<α<3,0<ξ1<ξ2<⋯<ξm-2<+∞, satisfies0<∑i=1m-2‍βiξiα-1<Γ(α),  and  F:[0,+∞)×ℝ×ℝ→𝒫(ℝ)is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values.


Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.


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