On the existence of solutions for some infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential equations

Abstract

Abstract By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative. We investigate the approximate solutions for two infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential problems. Finally, we analyze two examples to confirm our main results.

Keywords

• continued fraction
• contraction map
• fractional integro-differential equation
• infinite Caputo-Fabrizio fractional derivative