A better method to implement the alpha synapse function in MATLAB

I have implemented a leaky integrate and fire neuron system that gives output in the form of an alpha function `alpha = t/tau * exp(1 - (t/tau))`. However, the piece of code that I use to implement it takes up atleast 80% of the runtime (approximately 4s out of the total 5s). During the course of the program this prt gets called at least 30000 times while the `computealphasynapseoutput` function gets called at least 1.5 million times. So I want to reduce the runtime of this part. I have tried using `arrayfun` to implement it but that takes up a lot more time than this.

Can anyone please suggest a more efficient implementation for this code??

To implement the alpha synapse I used the following piece of code:

    % Get the identity of the currently active neurons
    idAllActiveNeuron = idAllActiveNeuron > 0;
    if any(idAllActiveNeuron) % Only run if atleast one neuron is active
        for iActiveNeuron = find(idAllActiveNeuron).' % run for each active neuron
            %%synapticOutputArray stores the synaptic output for each neuron for each time instant
            %%iIntegration is the time instant
            %%spikeTimesArray is a cell array that is composed of spike times for 
            % each neuron. So if I have 5 neurons and neuron 4 spikes twice 
            % while neuron 5 spikes once, spikeTimesArray would be something 
            % like {[], [], [], [0.0023, 0.0034], [0.0675]}
            %%integrationInstant would be a time value like 0.0810
            %%tau_syn stores the value of tau for each neuron

            synapticOutputArray(iActiveNeuron, iIntegration) = computealphasynapseoutput(spikeTimesArray{iActiveNeuron}, integrationInstant, tau_syn(iActiveNeuron));

        end % iActiveNeuron
    end

The function `computealphasynapse` is implemented as follows:

    function synapticOutput = computealphasynapseoutput(firingTime, integrationInstant, tauSyn)
    %%COMPUTEALPHASYNAPSEOUTPUT Calculates the synaptic output over all
    %previous spikes of the neuron at a particular time instant using the
    %alpha synapse function
    %
    % Usage:
    %   synapticOutput = computealphasynapseoutput(firingTime, integrationInstant, tauSyn)
    %
    % Inputs:
    %           firingTime: vector of previous firing times (in seconds)
    %   integrationInstant: current integration time instant (in seconds)
    %               tauSyn: synaptic time constant of the neuron (in seconds)
    %
    % Output:
    %   synapticOutput: Synaptic output of the neuron at current time summed
    %                   over all firing instances
    %

    % Calculate the time difference of firing from current time
    timeDifference = (integrationInstant - firingTime) / tauSyn;
    % Calculate and sum the synaptic output for each spike
    synapticOutput = sum(timeDifference .* exp(1 - timeDifference));

    end % computealphasynapseoutput