In this paper, we initially derive the equivalent fractional integral equation to $$\Psi $$ -Hilfer hybrid differential equations and through it, prove existence of a solution in weighted space. The paper’s primary objective is obtain estimates on derivative utilize it inequalities involving derivative. With assistance these inequalities, determine extremal solutions comparison theorems.

‎This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by u...

Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transport...

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields applied sciences. In present article, class q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for numerical solution distinct inclusions achieved h...

In this paper, we incorporate fuzzy reasoning in fractional-order PD controllers. The resulting fuzzy fractional PD controller is investigated in terms of its digital implementation and robustness. The combined features of both algorithms will result in a better control system performance. Also, the effectiveness and robustness of the new methodology is illustrated through an application exampl...

In this study, the existence and uniqueness of solution for a system consisting sequential fractional differential equations that contain Caputo–Hadamard (CH) derivative are verified. To study these solutions, some most important results from fixed point theorems in Banach space were used. A practical example is also given to support theoretical side was obtained.

Studies regarding the two dual notions are conducted in this paper using Riemann–Liouville fractional integral of q-hypergeometric function for obtaining certain fuzzy differential subordinations and superordinations. Fuzzy best dominants subordinants given theorems investigating superordinations, respectively. Moreover, corollaries stated by considering particular functions with known geometri...