Abstract
In this work, a new existence result is established for a nonlocal hybrid boundary value problem which contains one left Caputo and one right Riemann–Liouville fractional derivatives and integrals. The main result is proved by applying a new generalization of Darbo’s theorem associated with measures of noncompactness. Finally, an example to justify the theoretical result is also presented.
Highlights
Fractional differential equations have attracted a lot of attention from many research studies as they have played a key role in many basic sciences such as chemistry, control theory, biology, and other arenas [1,2,3]
Fractional differential equations can be extended by creating different types of boundary conditions
An existence result is obtained via a new extension of Darbo’s theorem associated with measures of noncompactness
Summary
Fractional differential equations have attracted a lot of attention from many research studies as they have played a key role in many basic sciences such as chemistry, control theory, biology, and other arenas [1,2,3]. R are continuous functions, and the denote both right and left Riemann–Liouville fractional integrals of orders p, q > 0, respectively. For some recent results for boundary value problems involving left or/and right fractional derivatives, we refer to the papers [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and references therein. We investigate the existence of solutions for the following hybrid boundary value problem which contains both left Caputo and right Riemann–Liouville fractional derivatives and integrals and nonlocal hybrid conditions of the form:. We present an example to illustrate the obtained result
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