Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions
ψ-Hilfer Fractional Implicit Differential Equation
Keywords:Fractional differential equations, Fractional derivatives, Mittag-Leffler functions, Ulam stability, Fixed point theorem.
In this paper, we study the class of boundary value problems for a nonlinear implicit fractional differential equation with periodic conditions involving a ψ-Hilfer fractional derivative. With the help of properties Mittag-Leffler functions, and fixed-point techniques, we establish the existence and uniqueness results, whereas the generalized Gronwall inequality is applied to get the stability results. Also, an example is provided to illustrate the obtained results.
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