The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...

Integral inequalities for ?-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented via operator. A novel parameterized auxiliary identity involving proposed differentiable mappings. By identity, we derive several Ostrowski whose absolute values It that the obtained outcomes exhibit classical c...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D ax+ f1(t, x) = v(t) + f2(t, x), lim t→a+ J1−q a x(t) = b1, where D a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville dif...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

This paper deals with a class of nonlinear fractional Sturm–Liouville boundary value problems. Each sub equation in the system is partial including second kinds Fredholm integral and p-Laplacian operator, simultaneously. Infinitely many solutions are derived due to perfect involvements calculus theory variational methods some simpler more easily verified assumptions.