Abstract
The authors obtain existence and uniqueness results for a nonlinear fractional pantograph boundary value problem containing a variable order Hadamard fractional derivative. This type of model is appropriate for applications involving processes that occur in strongly anomalous media. They also derive a generalized Lyapunov-type inequality for the problem considered. Their results are obtained by the fractional calculus and Krasnosel’skii’s fixed point theorem. An example is given to illustrate their approach.
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