A Fractional Analog of the Duhamel Principle

Mathematics Subject Classification: 35CXX, 26A33, 35S10

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

2000 Mathematics Subject Classification: 26A33, 33C45

A Fractional LC − RC Circuit

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

Suggestion from the Past?

Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Mathematics Subject Classification: 26A33, 31B10

Theorem for Series in Three-Parameter Mittag-Leffler Function

Mathematics Subject Classification 2010: 26A33, 33E12.