Abstract
We discuss the existence of solutions of initial value problems for a class of hybrid fractional neutral differential equations. To prove the main results, we use a hybrid fixed point theorem for the sum of three operators. We also derive the dependence of a solution on the initial data and present an example to illustrate the results.
Highlights
1 Introduction In the last two decades, many researchers attracted toward the study of fractional differential equations, motivated by their broad use in mathematical modeling
This class of hybrid fractional differential equations includes the perturbations of original differential equations in different ways
In this paper, we discuss the existence of a solution for the initial value problem for the hybrid fractional neutral integro-differential equation
Summary
In the last two decades, many researchers attracted toward the study of fractional differential equations, motivated by their broad use in mathematical modeling. Sitho et al [ ] discussed the existence of solutions by using the hybrid fixed point theorems of Dhage [ ] for the sum of three operators in a Banach algebra for the following initial value problems of a hybrid fractional integro-differential equations:. The existence and uniqueness of a solution for the problem of type cDγ + x(t) = f t, xt,c Dδ + xt , < t < , where cDγ + and cDδ + are Caputo derivatives with < γ < and < δ < , has already been proved by Niazi et al [ ] under some boundary conditions Motivated by these papers and the fact that the time-delay phenomenon is so common and certain. In this paper, we discuss the existence of a solution for the initial value problem for the hybrid fractional neutral integro-differential equation.
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