A non-local problem with discontinuous matching condition for loaded mixed type equation involving the Caputo fractional derivative

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+	On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity	1999	Kai Diethelm Alan D. Freed
+	Fractional Integrals and Derivatives: Theory and Applications	1993	Stefan Samko Anatoly A. Kilbas O. I. Marichev
+	Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics	2012	Francesco Mainardi
+	Theory and Applications of Fractional Differential Equations	2006	Anatoly A. Kilbas H. M. Srivastava Juan J. Trujillo
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+	Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)	2006	Anatoly A. Kilbas H. M. Srivástava Juan J. Trujillo
+	Solution of Boundary Value Problems for the Fractional Diffusion Equation by the Green Function Method	2003	А. В. Псху
+	A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations	2014	A. H. Bhrawy E. H. Doha Dumitru Băleanu S. S. Ezz‐Eldien
+	Fractional Calculus in Bioengineering	2007	Bruce J. West
+	Fractional-order diffusion-wave equation	1996	A. M. A. El‐Sayed