Existence and Ulam stability results for nonlinear hybrid implicit Caputo fractional differential equations. (English) Zbl 1474.34063

Summary: In this paper, we study the existence, uniqueness and estimate of solutions for nonlinear hybrid implicit Caputo fractional differential equations by using the contraction mapping principle and the generalization of Gronwall’s inequality. After that, we also establish the Ulam stability for the problem at hand. Finally, an example is given to illustrate this work.


34A09 Implicit ordinary differential equations, differential-algebraic equations
34A08 Fractional ordinary differential equations
34D10 Perturbations of ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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