Analysis of (<i>α</i>,<i>β</i>)-order coupled implicit Caputo fractional differential equations using topological degree method

Abstract

Abstract This article is devoted to establish the existence of solution of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mrow><m:mrow><m:mo>(</m:mo><m:mrow><m:mi>α</m:mi><m:mo>,</m:mo><m:mi>β</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:mrow></m:math> $\left(\alpha ,\beta \right)$ -order coupled implicit fractional differential equation with initial conditions, using Laplace transform method. The topological degree theory is used to obtain sufficient conditions for uniqueness and at least one solution of the considered system. Beside this, Ulam’s type stabilities are discussed for the proposed system. To support our main results, we present an example.