Line source diffraction by double strips with different fractional boundary conditions

In this study, the cylindrical wave diffraction by double strips with different lengths and boundary conditions are investigated. The scattered fields are found by the Numerical-Analytical Approach. The double-strip structure satisfies integral boundary conditions which are the generalization of Dirichlet and Neumann boundary conditions. The electric field, current distribution, and Total Radar Cross Sections are investigated. The results are compared with other methods and previous findings such as the Method of Moments and Physical Optics. The theoretical and numerical analyses indicate that the fractional order, the position of the line source have tremendous effects on the total-field distributions.

The Diffraction by the Half-plane with the Fractional Boundary Condition

In this article, there is considered the electromagnetic plane wave diffraction by the half-plane with fractional boundary conditions. As a mathematical tool, the fractional calculus is used. The theoretical part is given based on which the near field, Poynting vector and energy density distribution are calculated. Interesting results are obtained for the fractional order between marginal values, which describes a new type of material with new properties. The results are analyzed.

Analysis of some Katugampola fractional differential equations with fractional boundary conditions

<abstract><p>In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.</p></abstract>

Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions

This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).

Existence Solution for Nonlinear System of Fractional Integrodifferential Equations of Volterra Type with Fractional Boundary Conditions

This article investigates existence, uniqueness and stability solutions of new fractional Volterra integro-differential equations system with fractional boundary conditions by using the existence and uniqueness theorem. Theorems on existence and uniqueness of solution are established under some necessary and sufficient conditions on compact space. A simple example of application of the main results of this article is presented.

Hartman-Type and Lyapunov-Type Inequalities for a Fractional Differential Equation with Fractional Boundary Conditions

We prove Hartman-type and Lyapunov-type inequalities for a class of Riemann–Liouville fractional boundary value problems with fractional boundary conditions. Some applications including a lower bound for the corresponding eigenvalue problem are obtained.