In this paper, we study the existence and uniqueness of solutions for nonlinear fractional Katugampola differential equation with Erdely-Kober integral conditions, new results are established using Banach's contraction principle, contractions, Krasnoselskii's Leray-Schauder's fixed theorems. Four examples given in order to clarify theoretical results.

     Dx(t) + f(t, x(t), x(t)) = 0, t ∈ (0, 1), x(0) = ∫ 1 0 g0(s, x(s))ds, x(1) = ∫ 1 0 g1(s, x(s))ds, x(0) = 0, k = 2, 3, · · · , [α]− 1. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order α.

In this article, we establish fixed point results by defining the concept of F-Khan contraction an orthogonal set modifying symmetry usual contractive conditions. We also provide illustrative examples to support our results. The derived have been applied find analytical solutions integral equations. are verified with numerical simulation.

*Correspondence: [email protected] Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan Abstract We give characterizations of the contractive conditions, by using convergent sequences. Since we use a unified method, we can compare the contractive conditions very easily. We also discuss the contractive conditions of int...

Practical applications of microwave imaging often require the solution inverse scattering problems with inhomogeneous backgrounds. Toward this end, a novel inversion strategy, which combines multiscaling (MS) regularization scheme and difference contraction integral equation (DCIE) formulation, is proposed. Such an integrated approach mitigates nonlinearity ill-posedness problem to obtain relia...

There are many research available on the study of a real-valued fractal interpolation function and dimension its graph. In this paper, our main focus is to dimensional results for vector-valued Riemann–Liouville fractional integral. Here, we give some which ensure that functions quite different from functions. We determine interesting bounds Hausdorff graph function. also obtain associated inva...