• Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions 

  Djida, Jean Daniel; Fernández, Arran (MDPI, 2018)

  The Marchaud fractional derivative can be obtained as a Dirichlet-to–Neumann map via an extension problem to the upper half space. In this paper we prove interior Schauder regularity estimates for a degenerate elliptic ...

• Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique 

  Derbazi, Choukri; Baitiche, Zidane; Benchohra, Mouffak; Cabada Fernández, Alberto (MDPI, 2020)

  In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results ...

• Implicit Fractional Differential Equations via the Liouville–Caputo Derivative 

  Nieto Roig, Juan José; Ouahab, Abdelghani; Venktesh, Venktesh (MDPI, 2015)

  We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and ...

• Displacement Calculus 

  Márquez Albés, Ignacio; Fernández Tojo, Fernando Adrián (MDPI, 2020)

  In this work, we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and ...

• Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited 

  Fazli, Hossein; Sun, HongGuang; Nieto Roig, Juan José (MDPI, 2020)

  We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation ...

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