Publicación: (W,C)-PERIODIC FUNCTIONS AND MILD SOLUTIONS TO ABSTRACT FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS
Fecha
2018
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Electronic Journal of Qualitative Theory of Differential Equations
Resumen
IN THIS PAPER WE STUDY A NEW CLASS OF FUNCTIONS, WHICH WE CALL $(\OMEGA,C)$-PERIODIC FUNCTIONS. THIS COLLECTION INCLUDES PERIODIC, ANTI-PERIODIC, BLOCH AND UNBOUNDED FUNCTIONS. WE PROVE THAT THE SET CONFORMED BY THESE FUNCTIONS IS A BANACH SPACE WITH A SUITABLE NORM. FURTHERMORE, WE SHOW SEVERAL PROPERTIES OF THIS CLASS OF FUNCTIONS AS THE CONVOLUTION INVARIANCE. WE PRESENT SOME EXAMPLES AND A COMPOSITION RESULT. AS AN APPLICATION, WE ESTABLISH SOME SUFFICIENT CONDITIONS FOR THE EXISTENCE AND UNIQUENESS OF $(\OMEGA,C)$-PERIODIC MILD SOLUTIONS TO A FRACTIONAL EVOLUTION EQUATION.
