New Extension of Darbo’s Fixed Point Theorem and Its Application to a System of Weighted-Fractional-Type Integral Equations

Abstract

In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for a system of weighted fractional integral equations in Banach space BC(R+). At the end, we establish an example to show the applicability of our discovery.

Keywords

• F I E )%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> fractional integral equation (<named-content content-type="inline-formula"> <mml:math id="mm888"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="double-struck">F</mml:mi> <mml:mi mathvariant="double-struck">I</mml:mi> <mml:mi mathvariant="double-struck">E</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>)
• M N C )%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> measure of noncompactness (<named-content content-type="inline-formula"> <mml:math id="mm900"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="double-struck">M</mml:mi> <mml:mi mathvariant="double-struck">N</mml:mi> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>)
• F P T )%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> fixed point theorem (<named-content content-type="inline-formula"> <mml:math id="mm999"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="double-struck">F</mml:mi> <mml:mi mathvariant="double-struck">P</mml:mi> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>)
• D F P T )%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> Darbo’s fixed point theorem (<named-content content-type="inline-formula"> <mml:math id="mm1000"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="double-struck">D</mml:mi> <mml:mi mathvariant="double-struck">F</mml:mi> <mml:mi mathvariant="double-struck">P</mml:mi> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>)