scholarly journals Qualitative analysis of nonlinear coupled pantograph differential equations of fractional order with integral boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hussam Alrabaiah ◽  
Israr Ahmad ◽  
Kamal Shah ◽  
Ghaus Ur Rahman
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Qualitative Analysis ◽  
Fractional Order ◽  
Integral Boundary Conditions ◽  
Integral Boundary

Existence of solutions for fractional order impulsive differential equations with integral boundary conditions

2021 ◽  
pp. 002072092110020
Author(s):  
Rui Gao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Point Theorem ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Schauder Fixed Point ◽  
Schäuder Fixed Point Theorem

In this paper, we prove the expression and the existence of a class of nonlinear impulsive fractional order differential equations with integral boundary conditions. The unique solution of the differential equations by Green’s function is given. By using Schauder fixed point theorem and Leray-Schauder fixed point theorem, several sufficient conditions for the existence and uniqueness results are established.

scholarly journals On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hussein A. H. Salem ◽  
Mieczysław Cichoń
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Point Of View ◽  
Integral Boundary ◽  
Special Cases

The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.

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