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.

In this paper, we study the existence of solution for Hadamard Fractional Hybrid Differential equations with impulsive and nonlocal conditions. The main result is proved by means of a fixed point theorem. Finally, an example is also presented.

In this paper the authors prove existence, uniqueness and approximation of the solutions for initial value problems of nonlinear fractional differential equations with nonlocal conditions, using the operator theoretic technique in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partia...

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.

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...