In this article, we study a system of Hilfer (k,ψ)-fractional differential equations, subject to nonlocal boundary conditions involving (k,ψ)-derivatives and (k,ψ)-integrals. The results for the mentioned are established by using Mönch’s fixed point theorem, then Ulam–Hyers technique is used verify stability solution proposed system. general, symmetry fractional equations related each other. Wh...

Quasilinear equations in Banach spaces with distributed Gerasimov–Caputo fractional derivatives, which are defined by the Riemann–Stieltjes integrals, and a linear closed operator A, studied. The issues of unique solvability Cauchy problem to such considered. Under Lipschitz continuity condition phase variables two types over all nonlinear equation, we obtain versions on theorem nonlocal existe...

In R2, we consider an analytic family of fractional integrals , whose convolution kernel is obtained by taking some transverse derivatives of arclength measure on the parabola (t, t2) multiplied by |t|γ , and doing so in a homogeneous way. We determine the exact range of p, q for which the analytic family maps Lp to Lq . We also resolve a similar issue on the Heisenberg group.

This paper describes some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Browinian motion are defined and various properties of these integrals are given. A square integrab...

The paper discusses fractional integrals and derivatives appearing in the so-called (q, h)-calculus which is reduced for h = 0 to quantum calculus q 1 difference calculus. We introduce delta as well nabla version of these notions present their basic properties. Furthermore, we give comparisons with known results discuss possible extensions more general settings.

In the last few decades many authors pointed out that derivatives and integrals of non-integer order are very suitable for description properties various real problems. It has been shown fractional-order models more adequate than previously used integer-order models. this work, we aim to investigate different features plant virus model with its fractional equivalent. We present an application r...

Abstract In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence uniqueness of solution equation by using several fixed point theorems, also Ulam–Hyers stability solution. addition, study inclusion problem prove when multivalued map has convex values. give examples to ill...

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.