In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined. The iteration transform method solutions are obtained in series form to analyze the analytical results of fractional-order coupled Korteweg-de Vries equations. To understand the analytical procedure of Iteration transform method, some numerical problems are presented for the analytical result of fractional-order coupled Korteweg-de Vries equations. It is also demonstrated that the current technique’s solutions are in good agreement with the exact results. The numerical solutions show that only a few terms are sufficient for obtaining an approximate result, which is efficient, accurate, and reliable.

Fractional calculus operators are very useful in basic sciences and engineering. In this paper we study an integral operator which is directly related with many known fractional integral operators. A new generalized convexity namely exponentially (alpha, h-m)-convexity is defined which has been applied to obtain the bounds of unified integral operators. A generalized Hadamard inequality is established for the generalized convex functions. The established theorems reproduce several known results.