hybrid differential equation
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2021 ◽  
Vol 52 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Fahad Alsharari ◽  
Teh Yuan Ying

In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.


2021 ◽  
Vol 19 (1) ◽  
pp. 450-469
Author(s):  
Moosa Gabeleh ◽  
Deepesh Kumar Patel ◽  
Pradip Ramesh Patle ◽  
Manuel De La Sen

Abstract This work intends to treat the existence of mild solutions for the Hilfer fractional hybrid differential equation (HFHDE) with linear perturbation of first and second type in partially ordered Banach spaces. First, we establish the results concerning the actuality of fixed point of sum and product of operators via the concepts of measure of noncompactness and simulation functions in partially ordered spaces. Then combining these fixed point theorems with the concepts in fractional calculus, new existence results for mild solutions of HFHDE’s are established. Furthermore, the presented fixed point results and existence results improve and extend the present state-of-art in the literature. Competent examples in support of theory are illustrated for better understanding.


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shimaa I. Moustafa ◽  
Ayman Shehata

In this paper, we establish some fixed point results for α q s p -admissible mappings embedded in L -simulation functions in the context of b -metric-like spaces. As an application, we discuss the existence of a unique solution for fractional hybrid differential equation with multipoint boundary conditions via Caputo fractional derivative of order 1 < α ≤ 2 . Some examples and corollaries are also considered to illustrate the obtained results.


2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Said Melliani ◽  
Abdelati El Allaoui ◽  
Lalla Saadia Chadli

The aim of this paper is to study a boundary value problem of the hybrid differential equation with linear and nonlinear perturbations. It generalizes the existing problem of second type. The existence result is constructed using the Leray–Schauder alternative, and the uniqueness is guaranteed by Banach’s fixed-point theorem. Towards the end of this paper, an example is provided to illustrate the obtained results.


2012 ◽  
Vol 44 (2) ◽  
pp. 171-186 ◽  
Author(s):  
Bapurao Chandrabahan Dhage

In this paper, some basic results concerning the strict and nonstrict differential inequalities and existence of the maximal and minimal solutions are proved for a hybrid differential equation with linear perturbations of second type.


2012 ◽  
Vol 6 (1) ◽  
pp. 19 ◽  
Author(s):  
Brandi M Adams ◽  
Naleceia Davis ◽  
Paige Epps ◽  
Frederick Miller ◽  
DeAndrai Mullen ◽  
...  

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