Some remarks on sub-differential calculus

Some remarks on non-integer differential and integral calculus

Differential and integral calculus belongs to basic courses of mathematics and everybody understands geometrical and physical meaning of derivative or integral. But, hardly anybody can imagine for example derivative of order 1/2 or even of non-rational order. The branch of mathematics which generalizes calculus to non-integer case is known under the term “fractional calculs” although this name ...

Some Remarks on Linear Differential Systems*

Some Remarks on the Differential Transform Method

The differential transform method and Herrera’s complex integral method are shown to be related through the Taylor-Cauchy transform, which appears as a genuine fore-runner of both methods. A short discussion of this result is provided. Mathematics Subject Classification: 34A05, 34A25, 34A30, 34A34, 35C10

Some Remarks on Some Second-order Elliptic Differential Equations

We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type ü(s) + 2Bu̇(s) + Au(s) = f(s) (∗), where A, B are densely defined closed linear operators acting in a Hilbert space H and f : R 7→ H is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions; every solution to (∗) ...

Some Remarks on the Solvability of Some Abstract Differential Equations

This paper is concerned with the solvability of some abstract differential equation of type u̇(t) + Au(t) + Bu(t) ∋ f(t), t ∈ (0, T ], u(0) = 0, where A is a linear selfadjoint operator and B is a nonlinear (possibly multi-valued) maximal monotone operator in a real Hilbert space H with the normalization 0 ∈ B(0). We use the concept of variational sum introduced by H. Attouch, J.-B. Baillon, and...