Weak Solutions of Fractional Order Differential Equations via Volterra-Stieltjes Integral Operator
Journal Title: Journal of Mathematics and Applications - Year 2017, Vol 40, Issue
Abstract
The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics ([18], [21]). In this paper, we study the existence of weak solutions for fractional differential equations of Riemann-Liouville and Caputo types. We depend on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type in reflexive Banach spaces.
Authors and Affiliations
Ahmed M. A. El-Sayed, Wagdy G. El-Sayed, A. A. H. Abd El-Mowla
Keywords
Related Articles
- EP ID EP342920
- DOI 10.7862/rf.2017.6
- Views 68
- Downloads 0
Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells
Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4+ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transf...
On the Derivative of a Polynomial with Prescribed Zeros
For a polynomial [formula] of degree n having all its zeros in |z| ≤ K, K ≥ 1it is known that [formula]. By assuming a possible zero of order m, 0 ≤m ≤ n – 4, at z=0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have...
Ergodic Properties of Random Infinite Products of Nonexpansive Mappings
In this paper we are concerned with the asymptotic behavior of random (unrestricted) infinite products of nonexpansive selfmappings of closed and convex subsets of a complete hyperbolic space. In contrast with our previo...
Existence and Controllability Results for Sobolev-type Fractional Impulsive Stochastic Differential Equations with Infinite Delay
In this paper, we prove the existence of mild solutions for Sobolev-type fractional impulsive stochastic differential equations with infi nite delay in Hilbert spaces. In addition, the controllability of the system with...
On Some L_r-Biharmonic Euclidean Hypersurfaces
In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface x : M^n → E^{n+1} is said to be biharmonic if ∆^2x = 0, where ∆ is the Lapl...