Abstract
This article develops the existence theory for sequential fractional differential equations involving Caputo fractional derivative of order 1<alpha<2 with nonlocal integral boundary conditions. Examples are given to demonstrate applications of our results.
Highlights
1 Introduction Fractional calculus is a natural extension of ordinary calculus, where integrals and derivatives are defined for arbitrary real orders
The choice of an appropriate fractional derivative depends on the considered system, and for this reason, we find a large number of publications devoted to different fractional operators
To the best of our knowledge, the study of sequential fractional differential equations supplemented with four point nonlocal integral fractional boundary conditions has yet to be initiated
Summary
Fractional calculus is a natural extension of ordinary calculus, where integrals and derivatives are defined for arbitrary real orders. To the best of our knowledge, the study of sequential fractional differential equations supplemented with four point nonlocal integral fractional boundary conditions has yet to be initiated. Motivated by the above papers we establish the existence of solutions for the following nonlinear sequential fractional differential equation subject to nonlocal fractional integral conditions
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