Abstract
In the present paper, we investigate, using the Picard operator technique, some existence and Ulam type stability results for the Darboux problem associated to some partial fractional order differential inclusions.
Highlights
The fractional calculus deals with extensions of derivatives and integrals to noninteger orders
It represents a powerful tool in applied mathematics to study a myriad of problems from different fields of science and engineering, with many break-through results found in mathematical physics, finance, hydrology, biophysics, thermodynamics, control theory, statistical mechanics, astrophysics, cosmology and bioengineering [13, 24, 33]
The stability of functional equations was originally raised by Ulam in 1940 in a talk given at Wisconsin University
Summary
The fractional calculus deals with extensions of derivatives and integrals to noninteger orders. A. Rus (see [28,29,30] and their references) to study problems related to fixed point theory. Rus (see [28,29,30] and their references) to study problems related to fixed point theory This abstract approach was used later on by many mathematicians and it seemed to be a very useful and powerful method in the study of integral equations and inequalities, ordinary and partial differential equations (existence, uniqueness, differentiability of the solutions), etc. The theory of Picard operators is a very powerful tool in the study of Ulam–Hyers stability of functional equations. We only have to define a fixed point equation from the functional equation we want to study, if the defined operator is c-weakly Picard we have immediately the Ulam–Hyers stability of the desired equation.
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