Sentence examples for concept of solutions from inspiring English sources

At first, we give the concept of solutions for the initial-boundary value problem (2.8).

At present, the concept of solutions for impulsive fractional differential equations has been argued extensively.

At present, the concept of solutions for impulsive fractional differential equations [2 21] has been argued extensively.

We note that recently Agarwal et al. [13] have proposed the concept of solutions for fractional differential equations with uncertainty.

Finally, we agree with the second approach, which the concept of solutions for impulsive fractional differential equations has been given by (1.3).

Wang et al. [15, 16] discussed Ulam-Hyers stability for fractional equations and studied several types of such equations with various boundary value conditions as well, concept of solutions, existence results and examples are presented in [17].

Motivated by (1.6), we consider the following concept of solution.

This concept of solution is formally defined next.

Motivated by the results in [21], we consider the following concept of solution (or classical solution).

Thus, we need to introduce a concept of solution which is different from a classical solution.

We consider a differential equation of fractional order with uncertainty and present the concept of solution.