Abstract
In this paper, we investigate the existence of solutions for two nonlinear fractional multi-term integro-differential inclusions in two hybrid and non-hybrid versions. The boundary value conditions are in the form of three-point integral hybrid conditions. In this way, we define a new operator based on the integral solution of the given boundary value inclusion problem and then we use assumptions of a Dhage’s fixed point result for this fractional operator in the hybrid case. Also, the approximate endpoint property is applied for the corresponding set-valued maps in the non-hybrid case. Finally, we provide two examples to illustrate our main results.
Highlights
To design powerful computing software, we need strong mathematical tools
It is noted that the fractional hybrid multi-term integro-differential inclusion presented in this paper is new in the sense that the boundary value conditions are stated as three-point mixed Caputo integro-derivative hybrid conditions
5 Conclusion It is known that a lot of natural phenomena and processes in the world are modeled by different types of fractional differential equations and inclusions
Summary
To design powerful computing software, we need strong mathematical tools. In other words, if one can make exact patterns for natural phenomena and processes by using new mathematical formulas and operators, more flexible algorithms can be written in the software programming based on such relations and formulas. Many papers have been published by researchers, in which authors studied different properties of solutions for fractional hybrid boundary value problems. In 2016, Ahmad et al studied the existence of solutions for the nonlocal boundary value problem of fractional hybrid integro-differential inclusion
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