For simplicity, we adopt the following rules: a, b, x, y, z, X, Y , Z denote sets, n denotes a natural number, i denotes an integer, r, r1, r2, r3, s denote real numbers, c, c1, c2 denote complex numbers, and p denotes a point of En T. Let us observe that every element of IQ is irrational. Next we state a number of propositions: (1) If 0 ≤ r and 0 ≤ s and r2 = s2, then r = s. (2) If frac r ≥ fr...

Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on consideration appropriate equations (or systems equations). Here, differential are well-known be very useful instruments when building mathematical models - specially because that use derivatives offers several interpretations associated with real life laws. Differential class...

In this paper, we study the existence of solutions for fractional differential equations with Caputo-Hadamard derivative order 2 (1, 2]. The uniqueness result is proved via Banach’s contraction mapping principle and results are established by using Schauder’s fixed point theorem. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability proposed equation employed. Some examples given to illustrate r...

Borsuk-Ulam type theorems for arbitrary compact Lie group actions are proven. The transfer plays a major role in this approach. We present Borsuk-Ulam type theorems for arbitrary compact Lie group actions. The essence of our approach is a generalization of the ideal-valued index of FadellHusseini [FH88] using transfer [Boa66], [BG75], [Dol76], [KP72], [Rou71]. Once an appropriate concept (Defin...

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability solutions a coupled system fractional differential equations with Erdélyi–Kober Riemann–Liouville integral boundary conditions. Banach fixed point theorem used prove uniqueness solutions, while Leray–Schauder alternative existence solutions. Furthermore, we conclude that solution discussed problem Hyer...

The Borsuk-Ulam theorem and the Brouwer fixed point theorem are well-known theorems of topology with a very similar flavor. Both are non-constructive existence results with somewhat surprising conclusions. Most topology textbooks that cover these theorems (e.g., [4], [5], [6]) do not mention the two are related—although, in fact, the Borsuk-Ulam theorem implies the Brouwer Fixed Point Theorem. ...

Objectives. Optimizing glycemic control is crucial to prevent type 2 diabetes related complications. Cosmos caudatus is reported to have promising effect in improving plasma blood glucose in an animal model. However, its impact on human remains ambiguous. This study was carried out to evaluate the effectiveness of C. caudatus on glycemic status in patients with type 2 diabetes. Materials and Me...

In 1940 and in 1968 S. M. Ulam proposed the general problem:”When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941 D. H. Hyers solved this stability problem for linear mappings. In 1951 D. G. Bourgin was the second author to treat the same problem for additive mappings. According to...

Abstract In the current manuscript, we combine q -fractional integral operator and derivative to investigate a coupled hybrid fractional -differential systems with sequential -derivatives. The existence uniqueness of solutions for proposed system are established by means Leray-Schauder’s alternative Banach contraction principle. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability results discu...

In this paper, we investigate the generalizedHyers--Ulam stability of the functional equation